The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of dril...The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.展开更多
The high-speed winding spindle employs a flexible support system incorporating rubber O-rings.By precisely configuring the structural parameters and the number of the O-rings,the spindle can stably surpass its critica...The high-speed winding spindle employs a flexible support system incorporating rubber O-rings.By precisely configuring the structural parameters and the number of the O-rings,the spindle can stably surpass its critical speed points and maintain operational stability across the entire working speed range.However,the support stiffness and damping of rubber O-rings exhibit significant nonlinear frequency dependence.Conventional experimental methods for deriving equivalent stiffness and damping,based on the principle of the forced non-resonance method,require fabricating custom setups for each O-ring specification and conducting vibration tests at varying frequencies,resulting in low efficiency and high costs.This study proposes a hybrid simulation-experimental method for dynamic parameter identification.Firstly,the frequency-dependent dynamic parameters of a specific O-ring support system are experimentally obtained.Subsequently,a corresponding parametric finite element model is established to simulate and solve the equivalent elastic modulus and equivalent stiffness-damping coefficient of this O-ring support system.Ultimately,after iterative simulation,the simulated and experimental results achieve a 99.7%agreement.The parametric finite element model developed herein can directly simulate and inversely estimate frequency-dependent dynamic parameters for O-rings of different specifications but identical elastic modulus.展开更多
The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of t...The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.展开更多
In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical a...In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.展开更多
This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-...This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.展开更多
0 INTRODUCTION In recent years,modern railways have been actively under construction in the complex mountainous area of Southwest China.However,rockfall poses a significant threat to both construction and operation ph...0 INTRODUCTION In recent years,modern railways have been actively under construction in the complex mountainous area of Southwest China.However,rockfall poses a significant threat to both construction and operation phases of railway projects(Yan et al.,2023;Chen et al.,2022;Fanos and Pradhan,2018).展开更多
In recent decades,control performance monitoring(CPM)has experienced remarkable progress in research and industrial applications.While CPM research has been investigated using various benchmarks,the historical data be...In recent decades,control performance monitoring(CPM)has experienced remarkable progress in research and industrial applications.While CPM research has been investigated using various benchmarks,the historical data benchmark(HIS)has garnered the most attention due to its practicality and effectiveness.However,existing CPM reviews usually focus on the theoretical benchmark,and there is a lack of an in-depth review that thoroughly explores HIS-based methods.In this article,a comprehensive overview of HIS-based CPM is provided.First,we provide a novel static-dynamic perspective on data-level manifestations of control performance underlying typical controller capacities including regulation and servo:static and dynamic properties.The static property portrays time-independent variability in system output,and the dynamic property describes temporal behavior driven by closed-loop feedback.Accordingly,existing HIS-based CPM approaches and their intrinsic motivations are classified and analyzed from these two perspectives.Specifically,two mainstream solutions for CPM methods are summarized,including static analysis and dynamic analysis,which match data-driven techniques with actual controlling behavior.Furthermore,this paper also points out various opportunities and challenges faced in CPM for modern industry and provides promising directions in the context of artificial intelligence for inspiring future research.展开更多
The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to ...The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.展开更多
This paper presents an evaluation method for the entropy-weighting of wind power clusters that comprehensively evaluates the allocation problems of wind power clusters by considering the correlation between indicators...This paper presents an evaluation method for the entropy-weighting of wind power clusters that comprehensively evaluates the allocation problems of wind power clusters by considering the correlation between indicators and the dynamic performance of weight changes.A dynamic layered sorting allocation method is also proposed.The proposed evaluation method considers the power-limiting degree of the last cycle,the adjustment margin,and volatility.It uses the theory of weight variation to update the entropy weight coefficients of each indicator in real time,and then performs a fuzzy evaluation based on the membership function to obtain intuitive comprehensive evaluation results.A case study of a large-scale wind power base in Northwest China was conducted.The proposed evaluation method is compared with fixed-weight entropy and principal component analysis methods.The results show that the three scoring trends are the same,and that the proposed evaluation method is closer to the average level of the latter two,demonstrating higher accuracy.The proposed allocation method can reduce the number of adjustments made to wind farms,which is significant for the allocation and evaluation of wind power clusters.展开更多
In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a gene...In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.展开更多
BACKGROUND Inflammatory bowel disease(IBD)is a common chronic intestinal inflammatory disease.High oxidative stress is a treatment target for IBD.Cerium oxide(CeO2)nanomaterials as nanozymes with antioxidant activity ...BACKGROUND Inflammatory bowel disease(IBD)is a common chronic intestinal inflammatory disease.High oxidative stress is a treatment target for IBD.Cerium oxide(CeO2)nanomaterials as nanozymes with antioxidant activity are potential drugs for the treatment of colitis.AIM To synthesize hollow cerium(H-CeO2)nanoparticles by one-step method and to validate the therapeutic efficacy of H-CeO2 in IBD.METHODS H-CeO2 was synthesized by one-step method and examined its characterization and nanoenzymatic activity.Subsequently,we constructed dextran sulfate so-dium(DSS)-induced colitis in mice to observe the effects of H-CeO2 on colonic inflammation.The effects of H-CeO2 on colon inflammation and reactive oxygen species(ROS)levels in IBD mice were detected by hematoxylin and eosin staining and dichlorofluorescein diacetate staining,respectively.Finally,the biological sa-fety of H-CeO2 on mice was evaluated by hematoxylin and eosin staining,blood routine,and blood biochemistry.RESULTS H-CeO2 nanoparticles prepared by the one-step method were uniform,monodi-sperse and hollow.H-CeO2 had a good ability to scavenge ROS,∙OH and∙OOH.H-CeO2 reduced DSS-induced decreases in body weight and colon length,colonic epithelial damage,inflammatory infiltration,and ROS accumulation.H-CeO2 administration reduced the disease activity index of DSS-induced animals from about 8 to 5.H-CeO2 had no significant effect on body weight,total platelet count,hemoglobin,white blood cell,and red blood cell counts in healthy mice.No significant damage to major organs was observed in healthy mice following H-CeO2 administration.CONCLUSION The one-step synthesis of H-CeO2 nanomaterials had good antioxidant activity,biosafety,and inhibited deve-lopment of DSS-induced IBD in mice by scavenging ROS.展开更多
The fly ash from waste incineration poses a serious threat to human health due to its high content of dioxins.Hydrothermal treatment is an efficient and clean method on the decomposition and detoxifying of fly ash.To ...The fly ash from waste incineration poses a serious threat to human health due to its high content of dioxins.Hydrothermal treatment is an efficient and clean method on the decomposition and detoxifying of fly ash.To study the degradation mechanism of dioxins,this paper uses molecular dynamics(MD)to simulate the hydrothermal reaction process of polychlorinated dibenzo-p-dioxins(PCDDs)under different conditions,and the degradation mechanism of PCDDs is obtained.The results show that the degradation of PCDDs includes two pathways:the first pathway is the substitution of Cl groups by hydroxyl groups to form low-chlorine substitution products through direct hydrogenation,and the second pathway is the formation of non-toxic benzene ring structures accompanied by the cleavage of C—O bonds.The two degradation pathways of PCDDs well explain the changes in toxicity before and after the hydrothermal treatment of fly ash,which is consistent with experimental results.This study provides theoretical guidance for the harmless treatment process of fly ash via hydrothermal method.展开更多
The dynamic performance of high-speed trains is significantly influenced by sudden changes in aerodynamic loads(ADLs)when exiting a tunnel in a windy environment.Focusing on a double-track tunnel under construction in...The dynamic performance of high-speed trains is significantly influenced by sudden changes in aerodynamic loads(ADLs)when exiting a tunnel in a windy environment.Focusing on a double-track tunnel under construction in a mountain railway,we established an aerodynamic model involving a train exiting the tunnel,and verified it in the Fluent environment.Overset mesh technology was adopted to characterize the train’s movement.The flow field involving the train,tunnel,and crosswinds was simulated using the Reynolds-averaged turbulence model.Then,we built a comprehensive train-track coupled dynamic model considering the influences of ADLs,to investigate the vehicles’dynamic responses.The aerodynamics and dynamic behaviors of the train when affected by crosswinds with different velocities and directions are analyzed and discussed.The results show that the near-wall side crosswind leads to sharper variations in ADLs than the far-wall side crosswind.The leading vehicle suffers from more severe ADLs than other vehicles,which worsens the wheel-rail interaction and causes low-frequency vibration of the car body.When the crosswind velocity exceeds 20 m/s,significant wheel-rail impacts occur,and the running safety of the train worsens rapidly.展开更多
This study explored the dynamic behaviors and fracturing mechanisms of flawed granite under split-Hopkinson pressure bar testing,focusing on factors like grain size and flaw dimensions.By means of digital image proces...This study explored the dynamic behaviors and fracturing mechanisms of flawed granite under split-Hopkinson pressure bar testing,focusing on factors like grain size and flaw dimensions.By means of digital image processing and the discrete element method,Particle Flow Code 2D(PFC2D)models were constructed based on real granite samples,effectively overcoming the limitations of prior studies that mainly relied on randomized parameters.The results illustrate that the crack distribution of granite is significantly influenced by grain size and flaw dimensions.Tension cracks predominate and mineral boundaries,such as between feldspar and quartz,become primary crack sites.Both flaw length and width critically affect the crack density,distribution,and dynamic strength of granite.Specifically,dynamic strength tends to decrease with the enlargement of flaws and increase with an increase in flaw angles up to 90°.展开更多
To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based...To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based on adaptive fractal dimension characterization.By analyzing the nonlinear characteristics of gas concentration data,an adaptive window fractal analysis method is introduced.Combined with boxcounting dimension and variation of box dimension metrics,a cross-scale dynamic warning model for disaster prevention is established.The implementation involves three key phases:First,wavelet denoising and interpolation methods are employed for raw data preprocessing,followed by validation of fractal characteristics.Second,an adaptive window cross-scale fractal dimension method is proposed to calculate the box-counting dimension of gas concentration,enabling effective capture of multi-scale complex features.Finally,dynamic threshold partitioning is achieved through membership functions and the 3σprinciple,establishing a graded classification standard for the mine gas disaster(MGD)index.Validated through engineering applications at Shoushan#1 Coal Mine in Henan Province,the results demonstrate that the adaptive window fractal dimension curve exhibits significantly enhanced fluctuation characteristics compared to fixed window methods,with local feature detection capability improved and warning accuracy reaching 86.9%.The research reveals that this model effectively resolves the limitations of traditional methods in capturing local features and dependency on subjective thresholds through multiindicator fusion and threshold optimization,providing both theoretical foundation and practical tool for coal mine gas outburst early warning.展开更多
Rolling noise is an important source of railway noise and depends also on the dynamic behaviour of a railway track.This is characterized by the point or transfer mobility and the track decay rate,which depend on a num...Rolling noise is an important source of railway noise and depends also on the dynamic behaviour of a railway track.This is characterized by the point or transfer mobility and the track decay rate,which depend on a number of track parameters.One possible reason for deviations between simulated and measured results for the dynamic track behaviour is the uncertainty of the value of some track parameters used as input for the simulation.This in turn results in an uncertainty in the simulation results.In this contribution,it is proposed to use the general transformation method to assess a uncertainty band for the results.Most relevant input parameters for determining the point input mobility and the track decay rate for a ballasted track are analysed with regard to the uncertainties and for the value of each an interval is determined.Then,the general transformation method is applied to four different simulation methods,working both in the frequency and time domains.For one example track,the resulting uncertainty bands are compared to one dataset with measurements for the point mobility and the track decay rate.In addition,a sensitivity analysis is performed to determine the parameters that significantly influence the overall result.While all four simulation methods produce broad uncertainty bands for the results,none did match the measured results for the point mobility and the track decay rate over the entire frequency range considered.Besides the large influence of the uncertain pad stiffness,it turned out that the rail wear is also a significant source of uncertainty of the results.Overall,it is demonstrated that the proposed approach allows assessing the influence of uncertain input parameters in detail.展开更多
Earthquakes may inflict varied levels of damage on mountains.Understanding the deformation properties of earthquake-damaged rock masses is critical for evaluating rocky slope stability over time.Taking the phyllite of...Earthquakes may inflict varied levels of damage on mountains.Understanding the deformation properties of earthquake-damaged rock masses is critical for evaluating rocky slope stability over time.Taking the phyllite of the Xinmo Village rockslide as the research object,the degradation features of the phyllite are investigated through laboratory tests,and a discrete-element numerical approach that fully accounts for the progressive rock deterioration is presented.The approach is then used to investigate the evolution characteristics of phyllite under various dynamic and static loading circumstances.Results show that the remaining strength of rock decreases with increasing dynamic cyclic loading(DCL)amplitude and times but increases with increasing frequency.As the dynamic damage degree increases,rock failure modes become more complex,and microcracks expand in a more preferential orientation,as well as a denser spatial distribution.Dynamic damage cracks act as the dominant paths for the macroscopic failure surface of the rock.The results indicate that the input energy and dissipated energy increase with fluctuating and linear trends with the advance of the DCL,respectively.The peak strain energy and acoustic emission(AE)magnitude decrease with increasing dynamic damage degrees,and the distribution of AE events displays temporal dispersion and spatial clustering characteristics,which is attributed to a decrease in the rock's potential for storing energy.展开更多
This study designs four types of liquid-filled cylindrical shell structures to investigate their protection characteristics against explosive shock waves and high-speed fragments.Bare charge and charge-driven prefabri...This study designs four types of liquid-filled cylindrical shell structures to investigate their protection characteristics against explosive shock waves and high-speed fragments.Bare charge and charge-driven prefabricated fragments are employed to examine the damage under blast shock waves and combined blast and fragments loading on various liquid-filled cylindrical shell structures.The test results are compared to numerical calculations and theoretical analysis for the structure's deformation,the liquid medium's movement,and the pressure waves'propagation characteristics under different liquid-filling methods.The results showed that the filling method influences the blast protection and the struc-ture's energy absorption performance.The external filling method reduces the structural deformation,and the internal filling method increases the damage effect.The gapped internal filling method improves the structure's energy absorption efficiency.The pressure wave loading on the liquid-filled cylindrical shell structure differs depending on filling methods.Explosive shock waves and high-speed fragments show a damage enhancement effect on the liquid-filled cylindrical shell structure,depending on the thickness of the internal liquid container layer.The specific impulse on the inner surface of the cylindrical shell positively correlates to the radial deformation of the cylindrical shell structure,and the external liquid layer limits the radial structural deformation.展开更多
Under external disturbances,the shear mechanical responses and debonding failure mechanisms at anisotropic interfaces of anchoring system composed of multiphase media are inherently difficult to characterize due to th...Under external disturbances,the shear mechanical responses and debonding failure mechanisms at anisotropic interfaces of anchoring system composed of multiphase media are inherently difficult to characterize due to the concealment nature of interfacial interactions.This study establishes an equivalent shear model for a bolt-resin-rock anchoring system and conducts direct shear tests under dynamic normal load(DNL)boundary from both laboratory experiments and discrete element method(DEM)simulations.The research investigates the influence of normal dynamic load amplitude(An)and rock type on shear strength parameters,elucidating the evolutionary characteristics and underlying mechanisms of shear load and normal displacement fluctuations induced by cyclic normal loading,with maximum shear load decreasing by 36.81%to 46.94%as An increases from 10%to 70%when rock type varies from coal to limestone.Through analysis of strain field evolution,the critical impact of rock type on localization of shear failure surface is revealed,with systematic summarization of differentiated wear characteristics,failure modes,and key controlling factors associated with shear failure surface.Mesoscopic investigations enabled by DEM simulations uncover the nonuniform distribution of contact force chains within the material matrix and across the anisotropic interfaces under various DNL boundaries,clarify rock type dependent crack propagation pathways,and quantitatively assess the damage extent of shear failure surface,with the anisotropic interface damage factor increasing from 34.9%to 56.6%as An rises from 10%to 70%,and decreasing from 49.6%to 23.4%as rock type varies from coal to limestone.展开更多
The dynamic response characteristics of scoliosis and kyphosis to vibration are currently unclear.The finite element method(FEM)was employed to study the vibration response of patients with idiopathic scoliosis and ky...The dynamic response characteristics of scoliosis and kyphosis to vibration are currently unclear.The finite element method(FEM)was employed to study the vibration response of patients with idiopathic scoliosis and kyphosis.The objective is to analyze the dynamic characteristics of idiopathic scoliosis and kyphosis using FEM.The finite element model of T1—S1 segments was established and verified using the CT scanning images.The established scoliosis and kyphosis models were verified statistically and dynamically.The finite element software Abaqus was utilized to analyze the mode,harmonic response,and transient dynamics of scoliosis and kyphosis.The first four natural frequencies extracted from modal analysis were 1.34,2.26,4.49 and 17.69 Hz respectively.Notably,the first three natural frequencies decreased with the increase of upper body mass.In harmonic response analysis,the frequency corresponding to the maximum amplitude in x direction was the first order natural frequency,and the frequency corresponding to the maximum amplitude in y and z directions was the second order natural frequency.At the same resonance frequency,the amplitude of the thoracic spine was larger relative to that of the lumbar spine.The time domain results of transient analysis showed that the displacement dynamic response of each segment presented cyclic response characteristics over time.Under 2.26 Hz excitation,the dynamic response of the research object appeared as resonance.The higher the degree of spinal deformity,the greater the fundamental frequency.The first three natural modes of scoliosis and kyphosis contain vibration components in the vertical direction.The second order natural frequency was the most harmful to patients with scoliosis and kyphosis.Under cyclic loading,the deformation of the thoracic cone exceeds that of the lumbar cone.展开更多
基金supported by the National Natural Science Foundation of China(52174003,52374008).
文摘The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.
基金National Key R&D Program of China(No.2017YFB1304000)Fundamental Research Funds for the Central Universities,China(No.2232023G-05-1)。
文摘The high-speed winding spindle employs a flexible support system incorporating rubber O-rings.By precisely configuring the structural parameters and the number of the O-rings,the spindle can stably surpass its critical speed points and maintain operational stability across the entire working speed range.However,the support stiffness and damping of rubber O-rings exhibit significant nonlinear frequency dependence.Conventional experimental methods for deriving equivalent stiffness and damping,based on the principle of the forced non-resonance method,require fabricating custom setups for each O-ring specification and conducting vibration tests at varying frequencies,resulting in low efficiency and high costs.This study proposes a hybrid simulation-experimental method for dynamic parameter identification.Firstly,the frequency-dependent dynamic parameters of a specific O-ring support system are experimentally obtained.Subsequently,a corresponding parametric finite element model is established to simulate and solve the equivalent elastic modulus and equivalent stiffness-damping coefficient of this O-ring support system.Ultimately,after iterative simulation,the simulated and experimental results achieve a 99.7%agreement.The parametric finite element model developed herein can directly simulate and inversely estimate frequency-dependent dynamic parameters for O-rings of different specifications but identical elastic modulus.
文摘The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.
基金supported by the National Natural Science Foundation of China(Nos.52401342 and 12572025)the Fundamental Research Funds for the Central Universities of China(Nos.D5000240076 and G2025KY05171)+1 种基金the Natural Science Basic Research Program of Shaanxi Province(No.2025JCYBMS-026)the Basic Research Programs of Taicang(No.TC2024JC36)。
文摘In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.
基金support from the National Natural Science Foundation of China(Grant Nos.52174123&52274222).
文摘This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.
基金supported by the Open Research Fund of Key Laboratory of Geological Hazards on Three Gorges Reservoir Area(China Three Gorges University),Ministry of Education(No.2022KDZ03)the Science and Technology Projects of Yunnan Provincial Science and Technology Department(No.202401AT070328)+1 种基金the Young talents project of“Xingdian Talent Support Program”in Yunnan Province(No.YNWR-QNBJ-2020-019)the Fund Project of China Academy of Railway Sciences Co.,Ltd.(No.2021YJ178)。
文摘0 INTRODUCTION In recent years,modern railways have been actively under construction in the complex mountainous area of Southwest China.However,rockfall poses a significant threat to both construction and operation phases of railway projects(Yan et al.,2023;Chen et al.,2022;Fanos and Pradhan,2018).
基金supported in part by the National Natural Science Foundation of China(62125306)Zhejiang Key Research and Development Project(2024C01163)the State Key Laboratory of Industrial Control Technology,China(ICT2024A06)
文摘In recent decades,control performance monitoring(CPM)has experienced remarkable progress in research and industrial applications.While CPM research has been investigated using various benchmarks,the historical data benchmark(HIS)has garnered the most attention due to its practicality and effectiveness.However,existing CPM reviews usually focus on the theoretical benchmark,and there is a lack of an in-depth review that thoroughly explores HIS-based methods.In this article,a comprehensive overview of HIS-based CPM is provided.First,we provide a novel static-dynamic perspective on data-level manifestations of control performance underlying typical controller capacities including regulation and servo:static and dynamic properties.The static property portrays time-independent variability in system output,and the dynamic property describes temporal behavior driven by closed-loop feedback.Accordingly,existing HIS-based CPM approaches and their intrinsic motivations are classified and analyzed from these two perspectives.Specifically,two mainstream solutions for CPM methods are summarized,including static analysis and dynamic analysis,which match data-driven techniques with actual controlling behavior.Furthermore,this paper also points out various opportunities and challenges faced in CPM for modern industry and provides promising directions in the context of artificial intelligence for inspiring future research.
基金supported by the major advanced research project of Civil Aerospace from State Administration of Science,Technology and Industry of China.
文摘The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.
基金supported by the National Natural Science Foundation of China(Grant No.52076038,U22B20112,No.52106238)the Fundamental Research Funds for Central Universities(No.423162,B230201051).
文摘This paper presents an evaluation method for the entropy-weighting of wind power clusters that comprehensively evaluates the allocation problems of wind power clusters by considering the correlation between indicators and the dynamic performance of weight changes.A dynamic layered sorting allocation method is also proposed.The proposed evaluation method considers the power-limiting degree of the last cycle,the adjustment margin,and volatility.It uses the theory of weight variation to update the entropy weight coefficients of each indicator in real time,and then performs a fuzzy evaluation based on the membership function to obtain intuitive comprehensive evaluation results.A case study of a large-scale wind power base in Northwest China was conducted.The proposed evaluation method is compared with fixed-weight entropy and principal component analysis methods.The results show that the three scoring trends are the same,and that the proposed evaluation method is closer to the average level of the latter two,demonstrating higher accuracy.The proposed allocation method can reduce the number of adjustments made to wind farms,which is significant for the allocation and evaluation of wind power clusters.
基金supported by the Swiss National Science Foundation(Grant No.189882)the National Natural Science Foundation of China(Grant No.41961134032)support provided by the New Investigator Award grant from the UK Engineering and Physical Sciences Research Council(Grant No.EP/V012169/1).
文摘In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.
文摘BACKGROUND Inflammatory bowel disease(IBD)is a common chronic intestinal inflammatory disease.High oxidative stress is a treatment target for IBD.Cerium oxide(CeO2)nanomaterials as nanozymes with antioxidant activity are potential drugs for the treatment of colitis.AIM To synthesize hollow cerium(H-CeO2)nanoparticles by one-step method and to validate the therapeutic efficacy of H-CeO2 in IBD.METHODS H-CeO2 was synthesized by one-step method and examined its characterization and nanoenzymatic activity.Subsequently,we constructed dextran sulfate so-dium(DSS)-induced colitis in mice to observe the effects of H-CeO2 on colonic inflammation.The effects of H-CeO2 on colon inflammation and reactive oxygen species(ROS)levels in IBD mice were detected by hematoxylin and eosin staining and dichlorofluorescein diacetate staining,respectively.Finally,the biological sa-fety of H-CeO2 on mice was evaluated by hematoxylin and eosin staining,blood routine,and blood biochemistry.RESULTS H-CeO2 nanoparticles prepared by the one-step method were uniform,monodi-sperse and hollow.H-CeO2 had a good ability to scavenge ROS,∙OH and∙OOH.H-CeO2 reduced DSS-induced decreases in body weight and colon length,colonic epithelial damage,inflammatory infiltration,and ROS accumulation.H-CeO2 administration reduced the disease activity index of DSS-induced animals from about 8 to 5.H-CeO2 had no significant effect on body weight,total platelet count,hemoglobin,white blood cell,and red blood cell counts in healthy mice.No significant damage to major organs was observed in healthy mice following H-CeO2 administration.CONCLUSION The one-step synthesis of H-CeO2 nanomaterials had good antioxidant activity,biosafety,and inhibited deve-lopment of DSS-induced IBD in mice by scavenging ROS.
基金financially supported by the Science and Technology Innovation Program of Hunan Province(2024AQ2008)。
文摘The fly ash from waste incineration poses a serious threat to human health due to its high content of dioxins.Hydrothermal treatment is an efficient and clean method on the decomposition and detoxifying of fly ash.To study the degradation mechanism of dioxins,this paper uses molecular dynamics(MD)to simulate the hydrothermal reaction process of polychlorinated dibenzo-p-dioxins(PCDDs)under different conditions,and the degradation mechanism of PCDDs is obtained.The results show that the degradation of PCDDs includes two pathways:the first pathway is the substitution of Cl groups by hydroxyl groups to form low-chlorine substitution products through direct hydrogenation,and the second pathway is the formation of non-toxic benzene ring structures accompanied by the cleavage of C—O bonds.The two degradation pathways of PCDDs well explain the changes in toxicity before and after the hydrothermal treatment of fly ash,which is consistent with experimental results.This study provides theoretical guidance for the harmless treatment process of fly ash via hydrothermal method.
基金National Natural Science Foundation of China(No.52388102)New Cornerstone Science Foundation through the Xplorer Prize.
文摘The dynamic performance of high-speed trains is significantly influenced by sudden changes in aerodynamic loads(ADLs)when exiting a tunnel in a windy environment.Focusing on a double-track tunnel under construction in a mountain railway,we established an aerodynamic model involving a train exiting the tunnel,and verified it in the Fluent environment.Overset mesh technology was adopted to characterize the train’s movement.The flow field involving the train,tunnel,and crosswinds was simulated using the Reynolds-averaged turbulence model.Then,we built a comprehensive train-track coupled dynamic model considering the influences of ADLs,to investigate the vehicles’dynamic responses.The aerodynamics and dynamic behaviors of the train when affected by crosswinds with different velocities and directions are analyzed and discussed.The results show that the near-wall side crosswind leads to sharper variations in ADLs than the far-wall side crosswind.The leading vehicle suffers from more severe ADLs than other vehicles,which worsens the wheel-rail interaction and causes low-frequency vibration of the car body.When the crosswind velocity exceeds 20 m/s,significant wheel-rail impacts occur,and the running safety of the train worsens rapidly.
基金National Natural Science Foundation of China,Grant/Award Number:52274131General Project of China Postdoctoral Science Foundation,Grant/Award Number:2023M742141Talent Introduction Project of Shandong University of Science and Technology,Grant/Award Number:0104060540171。
文摘This study explored the dynamic behaviors and fracturing mechanisms of flawed granite under split-Hopkinson pressure bar testing,focusing on factors like grain size and flaw dimensions.By means of digital image processing and the discrete element method,Particle Flow Code 2D(PFC2D)models were constructed based on real granite samples,effectively overcoming the limitations of prior studies that mainly relied on randomized parameters.The results illustrate that the crack distribution of granite is significantly influenced by grain size and flaw dimensions.Tension cracks predominate and mineral boundaries,such as between feldspar and quartz,become primary crack sites.Both flaw length and width critically affect the crack density,distribution,and dynamic strength of granite.Specifically,dynamic strength tends to decrease with the enlargement of flaws and increase with an increase in flaw angles up to 90°.
基金funded by the National Key Research and Development ProgramFund for Young Scientists(No.2021YFC2900400)+5 种基金the National Natural Science Foundation of China(No.52304123)Fundamental Research Funds for the Central Universities(No.2024CDJXY025)Sichuan-Chongqing Science and Technology Innovation Cooperation Program Project(No.CSTB2024TIAD-CYKJCXX0016)Postdoctoral Research Foundation of China(No.2023M730412)Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(No.GZB20230914)Chongqing Outstanding Youth Science Foundation Program(No.CSTB2023NSCQ-JQX0027)。
文摘To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based on adaptive fractal dimension characterization.By analyzing the nonlinear characteristics of gas concentration data,an adaptive window fractal analysis method is introduced.Combined with boxcounting dimension and variation of box dimension metrics,a cross-scale dynamic warning model for disaster prevention is established.The implementation involves three key phases:First,wavelet denoising and interpolation methods are employed for raw data preprocessing,followed by validation of fractal characteristics.Second,an adaptive window cross-scale fractal dimension method is proposed to calculate the box-counting dimension of gas concentration,enabling effective capture of multi-scale complex features.Finally,dynamic threshold partitioning is achieved through membership functions and the 3σprinciple,establishing a graded classification standard for the mine gas disaster(MGD)index.Validated through engineering applications at Shoushan#1 Coal Mine in Henan Province,the results demonstrate that the adaptive window fractal dimension curve exhibits significantly enhanced fluctuation characteristics compared to fixed window methods,with local feature detection capability improved and warning accuracy reaching 86.9%.The research reveals that this model effectively resolves the limitations of traditional methods in capturing local features and dependency on subjective thresholds through multiindicator fusion and threshold optimization,providing both theoretical foundation and practical tool for coal mine gas outburst early warning.
文摘Rolling noise is an important source of railway noise and depends also on the dynamic behaviour of a railway track.This is characterized by the point or transfer mobility and the track decay rate,which depend on a number of track parameters.One possible reason for deviations between simulated and measured results for the dynamic track behaviour is the uncertainty of the value of some track parameters used as input for the simulation.This in turn results in an uncertainty in the simulation results.In this contribution,it is proposed to use the general transformation method to assess a uncertainty band for the results.Most relevant input parameters for determining the point input mobility and the track decay rate for a ballasted track are analysed with regard to the uncertainties and for the value of each an interval is determined.Then,the general transformation method is applied to four different simulation methods,working both in the frequency and time domains.For one example track,the resulting uncertainty bands are compared to one dataset with measurements for the point mobility and the track decay rate.In addition,a sensitivity analysis is performed to determine the parameters that significantly influence the overall result.While all four simulation methods produce broad uncertainty bands for the results,none did match the measured results for the point mobility and the track decay rate over the entire frequency range considered.Besides the large influence of the uncertain pad stiffness,it turned out that the rail wear is also a significant source of uncertainty of the results.Overall,it is demonstrated that the proposed approach allows assessing the influence of uncertain input parameters in detail.
基金the financial support from the National Natural Science Foundation of China(Grant No.U22A20603)the National Key Research and Development Program of China(Grant No.2023YFC3008300).
文摘Earthquakes may inflict varied levels of damage on mountains.Understanding the deformation properties of earthquake-damaged rock masses is critical for evaluating rocky slope stability over time.Taking the phyllite of the Xinmo Village rockslide as the research object,the degradation features of the phyllite are investigated through laboratory tests,and a discrete-element numerical approach that fully accounts for the progressive rock deterioration is presented.The approach is then used to investigate the evolution characteristics of phyllite under various dynamic and static loading circumstances.Results show that the remaining strength of rock decreases with increasing dynamic cyclic loading(DCL)amplitude and times but increases with increasing frequency.As the dynamic damage degree increases,rock failure modes become more complex,and microcracks expand in a more preferential orientation,as well as a denser spatial distribution.Dynamic damage cracks act as the dominant paths for the macroscopic failure surface of the rock.The results indicate that the input energy and dissipated energy increase with fluctuating and linear trends with the advance of the DCL,respectively.The peak strain energy and acoustic emission(AE)magnitude decrease with increasing dynamic damage degrees,and the distribution of AE events displays temporal dispersion and spatial clustering characteristics,which is attributed to a decrease in the rock's potential for storing energy.
基金the National Natural Science Foundation of China(Grant Nos.52371342,52271338,52101378 and 51979277)。
文摘This study designs four types of liquid-filled cylindrical shell structures to investigate their protection characteristics against explosive shock waves and high-speed fragments.Bare charge and charge-driven prefabricated fragments are employed to examine the damage under blast shock waves and combined blast and fragments loading on various liquid-filled cylindrical shell structures.The test results are compared to numerical calculations and theoretical analysis for the structure's deformation,the liquid medium's movement,and the pressure waves'propagation characteristics under different liquid-filling methods.The results showed that the filling method influences the blast protection and the struc-ture's energy absorption performance.The external filling method reduces the structural deformation,and the internal filling method increases the damage effect.The gapped internal filling method improves the structure's energy absorption efficiency.The pressure wave loading on the liquid-filled cylindrical shell structure differs depending on filling methods.Explosive shock waves and high-speed fragments show a damage enhancement effect on the liquid-filled cylindrical shell structure,depending on the thickness of the internal liquid container layer.The specific impulse on the inner surface of the cylindrical shell positively correlates to the radial deformation of the cylindrical shell structure,and the external liquid layer limits the radial structural deformation.
基金support from the National Natural Science Foundation of China(Nos.51504247,52174092,51904290,and 52074259)the Natural Science Foundation of Jiangsu Province,China(No.BK20220157)+1 种基金the Fundamental Research Funds for the Central Universities,China(No.2022YCPY0202)the China University of Mining and Technology(CUMT)Open Sharing Fund for Large-scale Instruments and Equipment(No.DYGX-2025-47)is gratefully acknowledged.
文摘Under external disturbances,the shear mechanical responses and debonding failure mechanisms at anisotropic interfaces of anchoring system composed of multiphase media are inherently difficult to characterize due to the concealment nature of interfacial interactions.This study establishes an equivalent shear model for a bolt-resin-rock anchoring system and conducts direct shear tests under dynamic normal load(DNL)boundary from both laboratory experiments and discrete element method(DEM)simulations.The research investigates the influence of normal dynamic load amplitude(An)and rock type on shear strength parameters,elucidating the evolutionary characteristics and underlying mechanisms of shear load and normal displacement fluctuations induced by cyclic normal loading,with maximum shear load decreasing by 36.81%to 46.94%as An increases from 10%to 70%when rock type varies from coal to limestone.Through analysis of strain field evolution,the critical impact of rock type on localization of shear failure surface is revealed,with systematic summarization of differentiated wear characteristics,failure modes,and key controlling factors associated with shear failure surface.Mesoscopic investigations enabled by DEM simulations uncover the nonuniform distribution of contact force chains within the material matrix and across the anisotropic interfaces under various DNL boundaries,clarify rock type dependent crack propagation pathways,and quantitatively assess the damage extent of shear failure surface,with the anisotropic interface damage factor increasing from 34.9%to 56.6%as An rises from 10%to 70%,and decreasing from 49.6%to 23.4%as rock type varies from coal to limestone.
基金the National Natural Science Foundation of China(No.32260235)。
文摘The dynamic response characteristics of scoliosis and kyphosis to vibration are currently unclear.The finite element method(FEM)was employed to study the vibration response of patients with idiopathic scoliosis and kyphosis.The objective is to analyze the dynamic characteristics of idiopathic scoliosis and kyphosis using FEM.The finite element model of T1—S1 segments was established and verified using the CT scanning images.The established scoliosis and kyphosis models were verified statistically and dynamically.The finite element software Abaqus was utilized to analyze the mode,harmonic response,and transient dynamics of scoliosis and kyphosis.The first four natural frequencies extracted from modal analysis were 1.34,2.26,4.49 and 17.69 Hz respectively.Notably,the first three natural frequencies decreased with the increase of upper body mass.In harmonic response analysis,the frequency corresponding to the maximum amplitude in x direction was the first order natural frequency,and the frequency corresponding to the maximum amplitude in y and z directions was the second order natural frequency.At the same resonance frequency,the amplitude of the thoracic spine was larger relative to that of the lumbar spine.The time domain results of transient analysis showed that the displacement dynamic response of each segment presented cyclic response characteristics over time.Under 2.26 Hz excitation,the dynamic response of the research object appeared as resonance.The higher the degree of spinal deformity,the greater the fundamental frequency.The first three natural modes of scoliosis and kyphosis contain vibration components in the vertical direction.The second order natural frequency was the most harmful to patients with scoliosis and kyphosis.Under cyclic loading,the deformation of the thoracic cone exceeds that of the lumbar cone.
