In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regiona...In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.展开更多
Deep-sea mineral resource transportation predominantly utilizes hydraulic pipeline methodology.Environmental factors induce vibrations in flexible pipelines,thereby affecting the internal flow characteristics.Therefor...Deep-sea mineral resource transportation predominantly utilizes hydraulic pipeline methodology.Environmental factors induce vibrations in flexible pipelines,thereby affecting the internal flow characteristics.Therefore,real-time monitoring of solid–liquid two-phase flow in pipelines is crucial for system maintenance.This study develops an autoencoder-based deep learning framework to reconstruct three-dimensional solid–liquid two-phase flow within flexible vibrating pipelines utilizing sparse wall information from sensors.Within this framework,separate X-model and F-model with distinct hidden-layer structures are established to reconstruct the coordinates and flow field information on the computational domain grid of the pipeline under traveling wave vibration.Following hyperparameter optimization,the models achieved high reconstruction accuracy,demonstrating R^(2)values of 0.990 and 0.945,respectively.The models’robustness is evaluated across three aspects:vibration parameters,physical fields,and vibration modes,demonstrating good reconstruction performance.Results concerning sensors show that 20 sensors(0.06%of total grids)achieve a balance between accuracy and cost,with superior accuracy obtained when arranged along the full length of the pipe compared to a dense arrangement at the front end.The models exhibited a signal-to-noise ratio tolerance of approximately 27 dB,with reconstruction accuracy being more affected by sensor failures at both ends of the pipeline.展开更多
Fluorescent probes based on intramolecular charge transfer(ICT) have obvious advantages for accurate quantitative analysis.To obtain high-performance ratiometric probes requires distinct photophysical properties durin...Fluorescent probes based on intramolecular charge transfer(ICT) have obvious advantages for accurate quantitative analysis.To obtain high-performance ratiometric probes requires distinct photophysical properties during recognition reaction process,which is closely related to their ICT characteristics.1,8-Naphthalimide is known as a typical fluorophore with desirable ICT property when functionalized with an electron-donating moiety at the para-position of the naphthalene chromophore.Although the photophysical properties of para-substituted 1,8-naphthalimide have been well studied,its meta-substituted counterpart has not been fully evaluated since the meta-position is conventionally thought to be weakly conjugated.Herein,combined experimental and theoretical studies are performed which consistently indicate that stronger charge transfer(CT) is exhibited by the meta-amino substituted 1,8-naphthalimide(m-NH_(2)) compared to the para-amino substituted one(p-NH_(2)).The ratiometric response of fluorescence with significant changes in wavelength and intensity upon acetylation(m-NAc and p-NAc) can be attributed to the larger ICT and stronger-NH_(2) vibrations.This observation is further demonstrated by deuterium oxide experiments,viscosity experiments and quantum chemical calculations.The practical application of meta-amino-1,8-naphthalimide ICT-based probes is also confirmed.This research is expected to bring an in-depth understanding of π-conjugated systems with ICT characteristics,and facilitates the design of sensitive ICT fluorescent probes with meta-amino substitution.展开更多
Two-dimensional phononic crystal(PnC)slabs have shown advantages in enhancing the quality factors Q of piezoelectric laterally vibrating resonators(LVRs)through topology optimization.However,the narrow geometries of m...Two-dimensional phononic crystal(PnC)slabs have shown advantages in enhancing the quality factors Q of piezoelectric laterally vibrating resonators(LVRs)through topology optimization.However,the narrow geometries of most topology-optimized silicon–air 2D PnC slabs face significant fabrication challenges owing to restricted etching precision,and the anisotropic nature of silicon is frequently overlooked.To address these issues,this study employs the finite element method with appropriate discretization numbers and the genetic algorithm to optimize the structures and geometries of 2D silicon–air PnC slabs.The optimized square-lattice PnC slabs,featuring a rounded-cross structure oriented along the`110e directions of silicon,achieve an impressive relative bandgap(RBG)width of 82.2%for in-plane modes.When further tilted by 15° from the (100) directions within the(001)plane,the optimal RBG width is expanded to 91.4%.We fabricate and characterize thin-film piezoelectric-on-silicon LVRs,with or without optimized 2D PnC slabs.The presence of PnC slabs around anchors increases the series and parallel quality factors Q_(s) and Q_(p) from 2240 to 7118 and from 2237 to 7501,respectively,with the PnC slabs oriented along the`110e directions of silicon.展开更多
Under the condition of frequent replacement of wind tunnel models,multiple types of wind tunnel models are fixed by a slender support sting with low stiffness damping.When excited by wind load,various models produce r...Under the condition of frequent replacement of wind tunnel models,multiple types of wind tunnel models are fixed by a slender support sting with low stiffness damping.When excited by wind load,various models produce random multi-dimensional vibration with different characteristics,which makes it impossible to obtain accurate and efficient aerodynamic data.Therefore,in order to ensure the reliable and efficient conduction of wind tunnel test,a wind-tunnel-modeladaptive vibration control method is proposed in this paper.First,the split type adaptive vibration suppression structure is designed.Second,the multi-dimensional vibration characteristic characterization method is derived and the vibration characteristic identification method of the system is designed.Then,a vibration state estimation model is established according to the identification results of vibration characteristics,and a multi-actuator cooperative control method based on vibration state estimation is constructed.Finally,a model-adaptive vibration control system is built,and vibration characteristics identification and hammer experiments are carried out for two types of typical models.The results show that the proposed model-adaptive vibration control method increases the equivalent damping ratio of pitch and yaw dimensions of the high-aspect-ratio class model by 8.19 times and 48.81 times,respectively.The equivalent damping ratio of pitch and yaw dimensions of the highslenderness-ratio class model is increased by 16.44 and 5.43 times,respectively.It provides a strong guarantee for the reliable and efficient development of multi-type wind tunnel test tasks.展开更多
This article presents the design of a microfabricated bio-inspired flapping-wing Nnano Aaerial Vvehicle(NAV),driven by an electromagnetic system.Our approach is based on artificial wings composed of rigid bodies conne...This article presents the design of a microfabricated bio-inspired flapping-wing Nnano Aaerial Vvehicle(NAV),driven by an electromagnetic system.Our approach is based on artificial wings composed of rigid bodies connected by compliant links,which optimise aerodynamic forces though replicating the complex wing kinematics of insects.The originality of this article lies in a new design methodology based on a triple equivalence between a 3D model,a multibody model,and a mass/spring model(0D)which reduces the number of parameters in the problem.This approach facilitates NAV optimisation by using only the mass/spring model,thereby simplifying the design process while maintaining high accuracy.Two wing geometries are studied and optimised in this article to produce large-amplitude wing motions(approximately 40^\circ),and enabling flapping and twisting motion in quadrature.The results are validated thanks to experimental measurements for the large amplitude and through finite element simulations for the combined motion,confirming the effectiveness of this strategy for a NAV weighing less than 40 mg with a wingspan of under 3 cm.展开更多
Inspired that kangaroo can buffer the impact and absorb vibration from the ground and keep the whole-body stable,an integrated kangaroo bio-inspired vibration suppression(IKBVS)structure considering vibration isolatio...Inspired that kangaroo can buffer the impact and absorb vibration from the ground and keep the whole-body stable,an integrated kangaroo bio-inspired vibration suppression(IKBVS)structure considering vibration isolation-absorption simultaneously is proposed for low/wide band frequency vibration control.Based on skeleton mass,articulation friction,and the synergistic action among skeleton,articulation,and muscle/tendon,a vibration suppression model with more biological basic characteristics is derived.The validity of model and method is confirmed,and the static and dynamic analysis of the IKBVS system is carried out to investigate the vibration suppression performance.The quasi-zero stiffness region can be achieved with a smaller initial installation angle,medium rod length,smaller foot stiffness,and slightly lighter isolated mass in a wide displacement interval.The coupling mechanism of vibration isolation-absorption is revealed by parameter analysis.The results indicate that the IKBVS structure has favorite dynamic properties due to adjustable nonlinearity,namely,lower and adjustable resonance and anti-resonance frequency/peak and different levels of vibration suppression effect in high-frequency range are achieved readily.This research provides new insight into application of bio-inspired vibration suppression structures in various engineering systems for better vibration control.展开更多
This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A...This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.展开更多
Tactile sensing of subcutaneous organ vibrations provides a promising route toward human-machine interfaces and wear-able diagnostics,particularly for voice rehabilitation and silent-speech communication.Here,we prese...Tactile sensing of subcutaneous organ vibrations provides a promising route toward human-machine interfaces and wear-able diagnostics,particularly for voice rehabilitation and silent-speech communication.Here,we present a bioinspired piezoelectric vibration sensor that mimics the graded stiffness and stress-based transduction mechanism of otolithic cilia in the human vestibular system.The device consists of a trapezoidal cantilever array with tip inertial masses,fabricated through a hybrid stereolithography 3D printing and laser micromachining process for rapid prototyping without cleanroom facilities.Finite-element modeling and experimental measurements demonstrate a fundamental resonance near 1.2 kHz,a 5%flat-bandwidth of 350 Hz,and an in-band charge sensitivity of 3.17 pC/g.A wearable proof-of-concept test further verifies the sensor's ability to reproducibly distinguish phoneme-specific vibration patterns in both time and frequency domains.This work establishes a foundation for bioinspired tactile sensing front-ends in wearable voice interfaces and other intelligent diagnostic systems integrated with machine-learning algorithms.展开更多
Excessive blasting-induced vibration during drilling-and-blasting excavation of deep tunnels can trigger geological hazards and compromise the stability of both the rock mass and support structures.This study focused ...Excessive blasting-induced vibration during drilling-and-blasting excavation of deep tunnels can trigger geological hazards and compromise the stability of both the rock mass and support structures.This study focused on the deep double-line Sejila Mountain tunnel to systematically analyze the spatial response of blasting-induced vibration and to develop a prediction model through field tests and numerical simulations.The results revealed that the presence of a cross passage significantly altered propagation paths and the spatial distribution of blasting-induced vibration velocity.The peak particle velocity(PPV)at the cross-passage corner was amplified by approximately 1.92 times due to wave reflection and geometric focusing.Blasting-induced vibration waves attenuated non-uniformly across the tunnel cross-section,where PPV on the blast-face side was 1.54–6.56 times higher than that on the opposite side.We propose an improved PPV attenuation model that accounts for the propagation path effect.This model significantly improved fitting accuracy and resolved anomalous parameter(k and a)estimates in traditional equations,thereby improving prediction reliability.Furthermore,based on the observed spatial distribution of blasting-induced vibration,optimal monitoring point placement and targeted vibration control measures for tunnel blasting were discussed.These findings provide a scientific basis for designing blasting schemes and vibration mitigation strategies in deep tunnels.展开更多
Vortex-induced vibration(VIV)of an underwater manipulator in pulsating flow presents a notable engineering problem in precise control due to the velocity variation in the flow.This study investigates the VIV response ...Vortex-induced vibration(VIV)of an underwater manipulator in pulsating flow presents a notable engineering problem in precise control due to the velocity variation in the flow.This study investigates the VIV response of an underwater manipulator subjected to pulsating flow,focusing on how different postures affect the behavior of the system.The effects of pulsating parameters and manipulator arrangement on the hydrodynamic coefficient,vibration response,motion trajectory,and vortex shedding behaviors were analyzed.Results indicated that the cross flow vibration displacement in pulsating flow increased by 32.14%compared to uniform flow,inducing a shift in the motion trajectory from a crescent shape to a sideward vase shape.In the absence of interference between the upper and lower arms,the lift coefficient of the manipulator substantially increased with rising pulsating frequency,reaching a maximum increment of 67.0%.This increase in the lift coefficient led to a 67.05%rise in the vibration frequency of the manipulator in the in-line direction.As the pulsating amplitude increased,the drag coefficient of the underwater manipulator rose by 36.79%,but the vibration frequency in the cross-flow direction decreased by 56.26%.Additionally,when the upper and lower arms remained in a state of mutual interference,the cross-flow vibration amplitudes of the upper and lower arms were approximately 1.84 and 4.82 times higher in a circular-elliptical arrangement compared to an elliptical-circular arrangement,respectively.Consequently,the flow field shifted from a P+S pattern to a disordered pattern,disrupting the regularity of the motion trajectory.展开更多
Since the view that the localized rail third-order bending mode can cause high-order polygonization(mainly 18-23)of high-speed train wheels was put forward in 2017,many scholars have attempted to link a connection bet...Since the view that the localized rail third-order bending mode can cause high-order polygonization(mainly 18-23)of high-speed train wheels was put forward in 2017,many scholars have attempted to link a connection between the localized rail bending modes and wheel polygonization phenomenon and polygonal wheel passing frequency.This paper first establishes a flexible track model considering the structural and parametric characteristics of fasteners,verifies the model by using vehicle tracking test data,then investigates the influence of fastener parameter matching on the localized rail bending modes,and obtains the following conclusions:(1)There is nearly a 1:1 mapping relationship between the localized rail bending modal frequency and polygonal wheel passing(PWP)frequency,which supports that the localized rail bending mode is one of the causes of wheel polygonization.(2)The iron plate of the fastener system plays a role of dynamic vibration absorber in the vehicle-rail coupled system,and the fastener parameters significantly influence the localized rail bending modal vibration.Finally,this paper proposes a design principle of a high-frequency vibration-absorbing fastener,which provides a feasible solution to mitigate the localized rail bending modal vibration and high-order wheel polygonization.Meanwhile,it points out that this measure may induce other high-frequency vibration problems,e.g.,aggravating modal vibration above 800 Hz.Further,this paper proposes a concept of differentiated arrangement of fasteners,suggesting that different high-frequency vibration-absorbing fasteners be installed in different sections of the whole line to make the localized rail bending modal frequency of the whole line disordered,thus disrupting and further mitigating the development of the wheel polygonization.展开更多
Time-delayed blasting is widely utilized in engineering to mitigate induced vibration hazards and enhance fragmentation.The underlying vibration reduction principle is the decrease of the charge weight per delay,while...Time-delayed blasting is widely utilized in engineering to mitigate induced vibration hazards and enhance fragmentation.The underlying vibration reduction principle is the decrease of the charge weight per delay,while the potential for further vibration reduction remains debated,largely due to unclear underlying mechanisms.In light of the popularization of electronic detonators and the representativeness of double-hole configurationsfor multiple blastholes,it is essential to investigate the vibration characteristics induced by time-delayed double blastholes.Therefore,a series of doubleborehole experimental blasts was conducted in an underground roadway to clarify the variation in vibration from single-hole to dual-hole conditions.Based on the experimental data and inherent limitations,an exact full-fieldtheoretical model was further employed to systematically analyze the effects of delay time,charge length,and borehole inclination angle on vibrations induced by various doublehole configurations.The experimental data and theoretical analysis reveal that the general scaled distance effectively predicts vibrations in delayed blasting but does not reflectvibration reduction.Increasing delay time causes fluctuatingPPVs,which stabilize slightly above single-hole PPVs as delay times exceed a certain value.The delayed blasting primarily reduces near-fieldfrequencies.Longer charge lengths in double boreholes increase PPV levels and attenuation rates within a certain length,and the vibration behavior of combined long and short charge lengths is governed by the long blasthole.Larger blasthole inclination angles enhance vibration amplitude and reduce PPV attenuation rates.Optimizing inclination angles is more critical than adjusting delay times,and parallel boreholes offer the best vibration control.展开更多
With the continuous increase in performance requirements for power systems in the aerospace and low-altitude economy sectors,designing lightweight and highstrength blade structures with excellent dynamic characteristi...With the continuous increase in performance requirements for power systems in the aerospace and low-altitude economy sectors,designing lightweight and highstrength blade structures with excellent dynamic characteristics has become critical.This paper puts forward a dynamic model for a rotating functionally graded graphenereinforced(FG-GPR)sandwich metal porous cantilever pre-twisted plate(PTP),aiming to analyze its natural vibration characteristics.To this end,the mixture principle and the revised Halpin-Tsai model are used to determine the parameters of graphene and porosity distributions in the core layer.With the classical plate theory,the Rayleigh-Ritz method,and the polynomials,the dynamic equations are derived to solve for the free vibration mode shapes and frequencies of the rotating FG-GPR sandwich metal porous cantilever PTP.The comparison of natural frequencies and mode shapes with available literature results confirms the precision of the theoretical formulation and numerical computations.The bending stiffnesses are analyzed.Finally,the effects of different graphene/pore distributions,length-to-thickness/width ratios,layer thickness ratios,twist angles,and rotational speeds on the natural frequencies of the system are systematically investigated.展开更多
Traditional dynamic analysis of mechanical structures,often limited to individual beams or plates,fails to fully capture their dynamic behaviors.In systems where space and mass are constrained,such as the battery supp...Traditional dynamic analysis of mechanical structures,often limited to individual beams or plates,fails to fully capture their dynamic behaviors.In systems where space and mass are constrained,such as the battery support structures in electric aircraft,conventional absorbers and isolators are insufficient for effective vibration control.This study simplifies the battery support structure of electric aircraft as an integrated composite beam consisting of three interconnected beams,and investigated its structural dynamics properties and nonlinear vibration control under thermal conditions caused by battery heat.The nonlinear vibration control is performed using the Nitinol steel wire ropes(Ni Ti-ST),with nonlinear damping properties.The natural frequencies of system are determined using the Rayleigh-Ritz technique.Theoretical results are validated through both Finite Element Method(FEM)and hammer tests.Moreover,the dynamic equations are derived using the Lagrange method and discretized via the Galerkin Truncation Method(GTM).The Harmonic Balance Method(HBM)is used to evaluate the vibration responses of the integrated model,with further verification through the Runge-Kutta Method(RKM).The experiments are conducted to corroborate the theoretical analysis.The results show that the system frequency changes in stages with the increase of the stiffness of the integrated composite beam connection.Especially in the case of varying environments,as the temperature increases,the frequency of system will first increase to a certain maximum value and then gradually decrease.Furthermore,the NiTi-ST effectively reduces vibration in the integrated composite beam,particularly under varying temperatures and external excitations.展开更多
With the continuous development of the offshore wind industry,the design concept of composite foundation has been given attention in the past decade.This paper presents an accurate method for investigating the horizon...With the continuous development of the offshore wind industry,the design concept of composite foundation has been given attention in the past decade.This paper presents an accurate method for investigating the horizontal vibration of monopile-friction wheel composite foundations in layered saturated soil.Firstly,the three-dimensional continuum mechanics theory with the range of linear elasticity is introduced to calculate the frictional resistance distributed on the upper soil surface.Then,the resistances of multilayered soils and inviscid seawater to the pile shaft under horizontal harmonic excitation are obtained using Novak's plane strain model,Biot's porous media theory and radiationwave theory.Thirdly,the expressions for the deformation,bending moment and internal force of the Euler-Bernoulli pile are derived using the boundary conditions with definitephysical meaning and transfer matrix method.By comparing with the results of 1g laboratory test and the idealized formula reported by the literature,the rationality and accuracy of the developed dynamical model can be verified.Finally,this paper conducts a series of worked examples to investigate the influencesof the elastic modulus and thickness of three-layer saturated soil and the location of interlayer soil on the horizontal dynamic vibration of composite foundation.The results show that an increase in elastic modulus of the surface soil is an effective way to improve the dynamic stability of the composite foundation in service conditions.The conclusions drawn from the numerical examples can develop some guidelines for the current foundation design of offshore wind turbines.展开更多
Sandwich functionally graded(FG)auxetic beams are extensively utilized in aerospace,automotive,and biomedical industries due to their excellent strength-toweight ratio,impact resistance,and tunable mechanical properti...Sandwich functionally graded(FG)auxetic beams are extensively utilized in aerospace,automotive,and biomedical industries due to their excellent strength-toweight ratio,impact resistance,and tunable mechanical properties.The integration of FG materials with auxetic structures enhances their adaptability in advanced engineering applications.However,understanding their dynamic behavior under external excitations is essential for optimal design and structural reliability.Nonlinear interactions in such structures pose significant challenges in vibration analysis,necessitating robust analytical methods.This study presents a closed-form solution for the nonlinear forced vibration analysis of sandwich FG auxetic beams,offering an accurate and efficient method for predicting their dynamic response.The beam consists of two FG face sheets with material properties varying through the thickness and a re-entrant honeycomb auxetic core with an adjustable Poisson's ratio.The governing nonlinear equations of motion are derived using the first-order shear deformation theory(FSDT),the modified Gibson model,and the von Kármán relations,formulated through Hamilton's principle.A closed-form solution is obtained via the Galerkin method and multiple-scale technique.The results demonstrate that FG layers enable control of the overweight and dynamic response amplitude,with positive power law indexes reducing weight.Comparisons with finite element results confirm the accuracy of the proposed formulation.展开更多
A mechanical vibration technique to refine solidified microstructure was reported. Vibration energy was directly introduced into a molten alloy by a vibrating horn, and the vibrating horn was melted during vibration. ...A mechanical vibration technique to refine solidified microstructure was reported. Vibration energy was directly introduced into a molten alloy by a vibrating horn, and the vibrating horn was melted during vibration. Effects of vibration acceleration and mass ratio on the microstructure of Al-5% Cu alloy were investigated. Results show that the present mechanical vibration could provide localized cooling by extracting heat from the interior of molten alloy, and the cooling rate is strongly dependent on vibration acceleration. It is difficult to refine the solidified microstructure when the treated alloy keeps full liquid state within the entire vibrating duration. Significantly refined microstructure was obtained by applying mechanical vibration during the initial stage of solidification. Moreover, mechanisms of grain refinement were discussed.展开更多
MEMS gyroscope is a new inertial navigation sensor,which can measure the input angular rate of sensitive axis using Coriolis effect.Compared to the conventional gyroscope,it owns many unique advantages.A novel structu...MEMS gyroscope is a new inertial navigation sensor,which can measure the input angular rate of sensitive axis using Coriolis effect.Compared to the conventional gyroscope,it owns many unique advantages.A novel structure of vibrating ring gyroscope is proposed and the finite element model of the oscillator is established based on MEMS technology.Through the modal analysis,the natural frequency and mode shapes of the oscillator are obtained.By analyzing the effects of the structural parameters on the mode shapes and frequency of the harmonic oscillator,the optimal design parameters are got.The frequency difference between the operating mode and the other modes is greater than 1kHz after optimization,which can avoid the frequency coupling of the operating mode and other vibrating modes of the oscillator.The simulation results show that the performance parameters of the ring structure meet the design requirements and have obvious advantages.展开更多
We derive the non-dimensional coupling equation of two exciters, including inertia coupling, stiffness coupling and load coupling. The concept of general dynamic symmetry is proposed to physically explain the synehron...We derive the non-dimensional coupling equation of two exciters, including inertia coupling, stiffness coupling and load coupling. The concept of general dynamic symmetry is proposed to physically explain the synehronisation of the two exciters, which stems from the load coupling that produces the torque of general dynamic symmetry to force the phase difference between the two exciters close to the angle of general dynamic symmetry. The condition of implementing synchronisation is that the torque of general dynamic symmetry is greater than the asymmetric torque of the two motors. A general Lyapunov function is constructed to derive the stability condition of synchronisation that the non-dimensional inertia coupling matrix is positive definite and all its elements are positive. Numeric results show that the structure of the vibrating system can guarantee the stability of synchronisation of the two exciters, and that the greater the distances between the installation positions of the two exciters and the mass centre of the vibrating system are, the stronger the ability of general dynamic symmetry is.展开更多
文摘In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.
基金financial support by the National Natural Science Foundation of China (Nos.52471293 and 12372270)the National Youth Science Foundation of China (Nos.52101322 and 52108375)+3 种基金the Program for Intergovernmental International S&T Cooperation Projects of Shanghai Municipality, China (Nos.24510711100 and 22160710200)The Oceanic Interdisciplinary Program of Shanghai Jiao Tong University (No.SL2022PT101)funded by the Open Fund of the State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology (No.LP2415)National Key R&D Program of China (No.2023YFC2811600)
文摘Deep-sea mineral resource transportation predominantly utilizes hydraulic pipeline methodology.Environmental factors induce vibrations in flexible pipelines,thereby affecting the internal flow characteristics.Therefore,real-time monitoring of solid–liquid two-phase flow in pipelines is crucial for system maintenance.This study develops an autoencoder-based deep learning framework to reconstruct three-dimensional solid–liquid two-phase flow within flexible vibrating pipelines utilizing sparse wall information from sensors.Within this framework,separate X-model and F-model with distinct hidden-layer structures are established to reconstruct the coordinates and flow field information on the computational domain grid of the pipeline under traveling wave vibration.Following hyperparameter optimization,the models achieved high reconstruction accuracy,demonstrating R^(2)values of 0.990 and 0.945,respectively.The models’robustness is evaluated across three aspects:vibration parameters,physical fields,and vibration modes,demonstrating good reconstruction performance.Results concerning sensors show that 20 sensors(0.06%of total grids)achieve a balance between accuracy and cost,with superior accuracy obtained when arranged along the full length of the pipe compared to a dense arrangement at the front end.The models exhibited a signal-to-noise ratio tolerance of approximately 27 dB,with reconstruction accuracy being more affected by sensor failures at both ends of the pipeline.
基金financially supported by National Key Research and Development Programs (Nos.2022YFD1700403 and 2023YFD1700303)National Natural Science Foundation of China (Nos.12274128 and 12250003)+2 种基金Shanghai Rising-Star Program (No.21QA1402600)the support of NYU-ECNU Center for Computational Chemistry at NYU Shanghaithe University of Bath and the Open Research Fund of the School of Chemistry and Chemical Engineering,Henan Normal University (No.2020ZD01) for support。
文摘Fluorescent probes based on intramolecular charge transfer(ICT) have obvious advantages for accurate quantitative analysis.To obtain high-performance ratiometric probes requires distinct photophysical properties during recognition reaction process,which is closely related to their ICT characteristics.1,8-Naphthalimide is known as a typical fluorophore with desirable ICT property when functionalized with an electron-donating moiety at the para-position of the naphthalene chromophore.Although the photophysical properties of para-substituted 1,8-naphthalimide have been well studied,its meta-substituted counterpart has not been fully evaluated since the meta-position is conventionally thought to be weakly conjugated.Herein,combined experimental and theoretical studies are performed which consistently indicate that stronger charge transfer(CT) is exhibited by the meta-amino substituted 1,8-naphthalimide(m-NH_(2)) compared to the para-amino substituted one(p-NH_(2)).The ratiometric response of fluorescence with significant changes in wavelength and intensity upon acetylation(m-NAc and p-NAc) can be attributed to the larger ICT and stronger-NH_(2) vibrations.This observation is further demonstrated by deuterium oxide experiments,viscosity experiments and quantum chemical calculations.The practical application of meta-amino-1,8-naphthalimide ICT-based probes is also confirmed.This research is expected to bring an in-depth understanding of π-conjugated systems with ICT characteristics,and facilitates the design of sensitive ICT fluorescent probes with meta-amino substitution.
基金supported by the National Natural Science Foundation of China(Grant No.52175552)the National Key RD Program of China(Grant Nos.2022YFB3205400 and 2022YFB3204300).
文摘Two-dimensional phononic crystal(PnC)slabs have shown advantages in enhancing the quality factors Q of piezoelectric laterally vibrating resonators(LVRs)through topology optimization.However,the narrow geometries of most topology-optimized silicon–air 2D PnC slabs face significant fabrication challenges owing to restricted etching precision,and the anisotropic nature of silicon is frequently overlooked.To address these issues,this study employs the finite element method with appropriate discretization numbers and the genetic algorithm to optimize the structures and geometries of 2D silicon–air PnC slabs.The optimized square-lattice PnC slabs,featuring a rounded-cross structure oriented along the`110e directions of silicon,achieve an impressive relative bandgap(RBG)width of 82.2%for in-plane modes.When further tilted by 15° from the (100) directions within the(001)plane,the optimal RBG width is expanded to 91.4%.We fabricate and characterize thin-film piezoelectric-on-silicon LVRs,with or without optimized 2D PnC slabs.The presence of PnC slabs around anchors increases the series and parallel quality factors Q_(s) and Q_(p) from 2240 to 7118 and from 2237 to 7501,respectively,with the PnC slabs oriented along the`110e directions of silicon.
基金supported in part by the National Natural Science Foundation of China(Nos.52475550,52305095)in part by the Key R&D Project of Liaoning Province,China(No.2023JH2/101800026)。
文摘Under the condition of frequent replacement of wind tunnel models,multiple types of wind tunnel models are fixed by a slender support sting with low stiffness damping.When excited by wind load,various models produce random multi-dimensional vibration with different characteristics,which makes it impossible to obtain accurate and efficient aerodynamic data.Therefore,in order to ensure the reliable and efficient conduction of wind tunnel test,a wind-tunnel-modeladaptive vibration control method is proposed in this paper.First,the split type adaptive vibration suppression structure is designed.Second,the multi-dimensional vibration characteristic characterization method is derived and the vibration characteristic identification method of the system is designed.Then,a vibration state estimation model is established according to the identification results of vibration characteristics,and a multi-actuator cooperative control method based on vibration state estimation is constructed.Finally,a model-adaptive vibration control system is built,and vibration characteristics identification and hammer experiments are carried out for two types of typical models.The results show that the proposed model-adaptive vibration control method increases the equivalent damping ratio of pitch and yaw dimensions of the high-aspect-ratio class model by 8.19 times and 48.81 times,respectively.The equivalent damping ratio of pitch and yaw dimensions of the highslenderness-ratio class model is increased by 16.44 and 5.43 times,respectively.It provides a strong guarantee for the reliable and efficient development of multi-type wind tunnel test tasks.
基金supported by ANR-ASTRID NANOFLY(ANR-19-ASTR-0023)and French AID(Defense Innovation Agency).
文摘This article presents the design of a microfabricated bio-inspired flapping-wing Nnano Aaerial Vvehicle(NAV),driven by an electromagnetic system.Our approach is based on artificial wings composed of rigid bodies connected by compliant links,which optimise aerodynamic forces though replicating the complex wing kinematics of insects.The originality of this article lies in a new design methodology based on a triple equivalence between a 3D model,a multibody model,and a mass/spring model(0D)which reduces the number of parameters in the problem.This approach facilitates NAV optimisation by using only the mass/spring model,thereby simplifying the design process while maintaining high accuracy.Two wing geometries are studied and optimised in this article to produce large-amplitude wing motions(approximately 40^\circ),and enabling flapping and twisting motion in quadrature.The results are validated thanks to experimental measurements for the large amplitude and through finite element simulations for the combined motion,confirming the effectiveness of this strategy for a NAV weighing less than 40 mg with a wingspan of under 3 cm.
基金supported by the Natural Science Foundation of China(Grant No.52275091)Natural Science Foundation of Liaoning Province(Grant No.2022-MS-125)+1 种基金Shenyang Natural Science Foundation(Grant No.23-503-6-02)Fundamental Research Funds for the Central Universities(Grant No.N2303011).
文摘Inspired that kangaroo can buffer the impact and absorb vibration from the ground and keep the whole-body stable,an integrated kangaroo bio-inspired vibration suppression(IKBVS)structure considering vibration isolation-absorption simultaneously is proposed for low/wide band frequency vibration control.Based on skeleton mass,articulation friction,and the synergistic action among skeleton,articulation,and muscle/tendon,a vibration suppression model with more biological basic characteristics is derived.The validity of model and method is confirmed,and the static and dynamic analysis of the IKBVS system is carried out to investigate the vibration suppression performance.The quasi-zero stiffness region can be achieved with a smaller initial installation angle,medium rod length,smaller foot stiffness,and slightly lighter isolated mass in a wide displacement interval.The coupling mechanism of vibration isolation-absorption is revealed by parameter analysis.The results indicate that the IKBVS structure has favorite dynamic properties due to adjustable nonlinearity,namely,lower and adjustable resonance and anti-resonance frequency/peak and different levels of vibration suppression effect in high-frequency range are achieved readily.This research provides new insight into application of bio-inspired vibration suppression structures in various engineering systems for better vibration control.
文摘This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.
文摘Tactile sensing of subcutaneous organ vibrations provides a promising route toward human-machine interfaces and wear-able diagnostics,particularly for voice rehabilitation and silent-speech communication.Here,we present a bioinspired piezoelectric vibration sensor that mimics the graded stiffness and stress-based transduction mechanism of otolithic cilia in the human vestibular system.The device consists of a trapezoidal cantilever array with tip inertial masses,fabricated through a hybrid stereolithography 3D printing and laser micromachining process for rapid prototyping without cleanroom facilities.Finite-element modeling and experimental measurements demonstrate a fundamental resonance near 1.2 kHz,a 5%flat-bandwidth of 350 Hz,and an in-band charge sensitivity of 3.17 pC/g.A wearable proof-of-concept test further verifies the sensor's ability to reproducibly distinguish phoneme-specific vibration patterns in both time and frequency domains.This work establishes a foundation for bioinspired tactile sensing front-ends in wearable voice interfaces and other intelligent diagnostic systems integrated with machine-learning algorithms.
基金financially supported by the National Natural Science Foundation of China(Nos.42577209 and U22A20239)the Key R&D Program of Hunan Province(No.2024WK2004)the Key Technologies for Accurate Diagnosis and Intelligent Prevention and Control of Slope Hazards in Open pit Mines,181 Major R&D projects of Metallurgical Corporation of China Ltd。
文摘Excessive blasting-induced vibration during drilling-and-blasting excavation of deep tunnels can trigger geological hazards and compromise the stability of both the rock mass and support structures.This study focused on the deep double-line Sejila Mountain tunnel to systematically analyze the spatial response of blasting-induced vibration and to develop a prediction model through field tests and numerical simulations.The results revealed that the presence of a cross passage significantly altered propagation paths and the spatial distribution of blasting-induced vibration velocity.The peak particle velocity(PPV)at the cross-passage corner was amplified by approximately 1.92 times due to wave reflection and geometric focusing.Blasting-induced vibration waves attenuated non-uniformly across the tunnel cross-section,where PPV on the blast-face side was 1.54–6.56 times higher than that on the opposite side.We propose an improved PPV attenuation model that accounts for the propagation path effect.This model significantly improved fitting accuracy and resolved anomalous parameter(k and a)estimates in traditional equations,thereby improving prediction reliability.Furthermore,based on the observed spatial distribution of blasting-induced vibration,optimal monitoring point placement and targeted vibration control measures for tunnel blasting were discussed.These findings provide a scientific basis for designing blasting schemes and vibration mitigation strategies in deep tunnels.
基金Supported by the National Natural Science Foundation of China(No.51905211)A Project of the“20 Regulations for New Universities”Funding Program of Jinan(No.202228116).
文摘Vortex-induced vibration(VIV)of an underwater manipulator in pulsating flow presents a notable engineering problem in precise control due to the velocity variation in the flow.This study investigates the VIV response of an underwater manipulator subjected to pulsating flow,focusing on how different postures affect the behavior of the system.The effects of pulsating parameters and manipulator arrangement on the hydrodynamic coefficient,vibration response,motion trajectory,and vortex shedding behaviors were analyzed.Results indicated that the cross flow vibration displacement in pulsating flow increased by 32.14%compared to uniform flow,inducing a shift in the motion trajectory from a crescent shape to a sideward vase shape.In the absence of interference between the upper and lower arms,the lift coefficient of the manipulator substantially increased with rising pulsating frequency,reaching a maximum increment of 67.0%.This increase in the lift coefficient led to a 67.05%rise in the vibration frequency of the manipulator in the in-line direction.As the pulsating amplitude increased,the drag coefficient of the underwater manipulator rose by 36.79%,but the vibration frequency in the cross-flow direction decreased by 56.26%.Additionally,when the upper and lower arms remained in a state of mutual interference,the cross-flow vibration amplitudes of the upper and lower arms were approximately 1.84 and 4.82 times higher in a circular-elliptical arrangement compared to an elliptical-circular arrangement,respectively.Consequently,the flow field shifted from a P+S pattern to a disordered pattern,disrupting the regularity of the motion trajectory.
基金supported by the National Natural Science Foundation of China(Grant Nos.:52202423,U2268211,and 52475136)the China Postdoctoral Science Foundation(Grant Nos.:2022M712636 and 2023T160546)+1 种基金the Natural Science Foundation of Sichuan Province(Grant No.:2025ZNSFSC0398)the Independent R&D Project of the State Key Laboratory of Traction Power(Grant No.:2023TPL-T14).
文摘Since the view that the localized rail third-order bending mode can cause high-order polygonization(mainly 18-23)of high-speed train wheels was put forward in 2017,many scholars have attempted to link a connection between the localized rail bending modes and wheel polygonization phenomenon and polygonal wheel passing frequency.This paper first establishes a flexible track model considering the structural and parametric characteristics of fasteners,verifies the model by using vehicle tracking test data,then investigates the influence of fastener parameter matching on the localized rail bending modes,and obtains the following conclusions:(1)There is nearly a 1:1 mapping relationship between the localized rail bending modal frequency and polygonal wheel passing(PWP)frequency,which supports that the localized rail bending mode is one of the causes of wheel polygonization.(2)The iron plate of the fastener system plays a role of dynamic vibration absorber in the vehicle-rail coupled system,and the fastener parameters significantly influence the localized rail bending modal vibration.Finally,this paper proposes a design principle of a high-frequency vibration-absorbing fastener,which provides a feasible solution to mitigate the localized rail bending modal vibration and high-order wheel polygonization.Meanwhile,it points out that this measure may induce other high-frequency vibration problems,e.g.,aggravating modal vibration above 800 Hz.Further,this paper proposes a concept of differentiated arrangement of fasteners,suggesting that different high-frequency vibration-absorbing fasteners be installed in different sections of the whole line to make the localized rail bending modal frequency of the whole line disordered,thus disrupting and further mitigating the development of the wheel polygonization.
基金supported by the National Natural Science Foundation of China(Grant Nos.42407267 and 52374152)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20220975).
文摘Time-delayed blasting is widely utilized in engineering to mitigate induced vibration hazards and enhance fragmentation.The underlying vibration reduction principle is the decrease of the charge weight per delay,while the potential for further vibration reduction remains debated,largely due to unclear underlying mechanisms.In light of the popularization of electronic detonators and the representativeness of double-hole configurationsfor multiple blastholes,it is essential to investigate the vibration characteristics induced by time-delayed double blastholes.Therefore,a series of doubleborehole experimental blasts was conducted in an underground roadway to clarify the variation in vibration from single-hole to dual-hole conditions.Based on the experimental data and inherent limitations,an exact full-fieldtheoretical model was further employed to systematically analyze the effects of delay time,charge length,and borehole inclination angle on vibrations induced by various doublehole configurations.The experimental data and theoretical analysis reveal that the general scaled distance effectively predicts vibrations in delayed blasting but does not reflectvibration reduction.Increasing delay time causes fluctuatingPPVs,which stabilize slightly above single-hole PPVs as delay times exceed a certain value.The delayed blasting primarily reduces near-fieldfrequencies.Longer charge lengths in double boreholes increase PPV levels and attenuation rates within a certain length,and the vibration behavior of combined long and short charge lengths is governed by the long blasthole.Larger blasthole inclination angles enhance vibration amplitude and reduce PPV attenuation rates.Optimizing inclination angles is more critical than adjusting delay times,and parallel boreholes offer the best vibration control.
基金Project supported by the National Natural Science Foundation of China(Nos.12272056 and 11832002)。
文摘With the continuous increase in performance requirements for power systems in the aerospace and low-altitude economy sectors,designing lightweight and highstrength blade structures with excellent dynamic characteristics has become critical.This paper puts forward a dynamic model for a rotating functionally graded graphenereinforced(FG-GPR)sandwich metal porous cantilever pre-twisted plate(PTP),aiming to analyze its natural vibration characteristics.To this end,the mixture principle and the revised Halpin-Tsai model are used to determine the parameters of graphene and porosity distributions in the core layer.With the classical plate theory,the Rayleigh-Ritz method,and the polynomials,the dynamic equations are derived to solve for the free vibration mode shapes and frequencies of the rotating FG-GPR sandwich metal porous cantilever PTP.The comparison of natural frequencies and mode shapes with available literature results confirms the precision of the theoretical formulation and numerical computations.The bending stiffnesses are analyzed.Finally,the effects of different graphene/pore distributions,length-to-thickness/width ratios,layer thickness ratios,twist angles,and rotational speeds on the natural frequencies of the system are systematically investigated.
基金supported by the National Natural Science Foundation of China(No.12272240)the Liaoning Revitalization Talents Program,China(No.XLYC2203197)。
文摘Traditional dynamic analysis of mechanical structures,often limited to individual beams or plates,fails to fully capture their dynamic behaviors.In systems where space and mass are constrained,such as the battery support structures in electric aircraft,conventional absorbers and isolators are insufficient for effective vibration control.This study simplifies the battery support structure of electric aircraft as an integrated composite beam consisting of three interconnected beams,and investigated its structural dynamics properties and nonlinear vibration control under thermal conditions caused by battery heat.The nonlinear vibration control is performed using the Nitinol steel wire ropes(Ni Ti-ST),with nonlinear damping properties.The natural frequencies of system are determined using the Rayleigh-Ritz technique.Theoretical results are validated through both Finite Element Method(FEM)and hammer tests.Moreover,the dynamic equations are derived using the Lagrange method and discretized via the Galerkin Truncation Method(GTM).The Harmonic Balance Method(HBM)is used to evaluate the vibration responses of the integrated model,with further verification through the Runge-Kutta Method(RKM).The experiments are conducted to corroborate the theoretical analysis.The results show that the system frequency changes in stages with the increase of the stiffness of the integrated composite beam connection.Especially in the case of varying environments,as the temperature increases,the frequency of system will first increase to a certain maximum value and then gradually decrease.Furthermore,the NiTi-ST effectively reduces vibration in the integrated composite beam,particularly under varying temperatures and external excitations.
基金supported by the National Natural Science Foundation of China(Grant No.52178329),the China Scholarship Council(Grant No.202306130155)the Postgraduate Scientific Research Innovation Project of Hunan Province,China(Grant No.CX20230442).
文摘With the continuous development of the offshore wind industry,the design concept of composite foundation has been given attention in the past decade.This paper presents an accurate method for investigating the horizontal vibration of monopile-friction wheel composite foundations in layered saturated soil.Firstly,the three-dimensional continuum mechanics theory with the range of linear elasticity is introduced to calculate the frictional resistance distributed on the upper soil surface.Then,the resistances of multilayered soils and inviscid seawater to the pile shaft under horizontal harmonic excitation are obtained using Novak's plane strain model,Biot's porous media theory and radiationwave theory.Thirdly,the expressions for the deformation,bending moment and internal force of the Euler-Bernoulli pile are derived using the boundary conditions with definitephysical meaning and transfer matrix method.By comparing with the results of 1g laboratory test and the idealized formula reported by the literature,the rationality and accuracy of the developed dynamical model can be verified.Finally,this paper conducts a series of worked examples to investigate the influencesof the elastic modulus and thickness of three-layer saturated soil and the location of interlayer soil on the horizontal dynamic vibration of composite foundation.The results show that an increase in elastic modulus of the surface soil is an effective way to improve the dynamic stability of the composite foundation in service conditions.The conclusions drawn from the numerical examples can develop some guidelines for the current foundation design of offshore wind turbines.
文摘Sandwich functionally graded(FG)auxetic beams are extensively utilized in aerospace,automotive,and biomedical industries due to their excellent strength-toweight ratio,impact resistance,and tunable mechanical properties.The integration of FG materials with auxetic structures enhances their adaptability in advanced engineering applications.However,understanding their dynamic behavior under external excitations is essential for optimal design and structural reliability.Nonlinear interactions in such structures pose significant challenges in vibration analysis,necessitating robust analytical methods.This study presents a closed-form solution for the nonlinear forced vibration analysis of sandwich FG auxetic beams,offering an accurate and efficient method for predicting their dynamic response.The beam consists of two FG face sheets with material properties varying through the thickness and a re-entrant honeycomb auxetic core with an adjustable Poisson's ratio.The governing nonlinear equations of motion are derived using the first-order shear deformation theory(FSDT),the modified Gibson model,and the von Kármán relations,formulated through Hamilton's principle.A closed-form solution is obtained via the Galerkin method and multiple-scale technique.The results demonstrate that FG layers enable control of the overweight and dynamic response amplitude,with positive power law indexes reducing weight.Comparisons with finite element results confirm the accuracy of the proposed formulation.
基金Project(50804023)supported by the National Natural Science Foundation of ChinaProject(GJJ12032)supported by the Education Department of Jiangxi Province,China+1 种基金Project(20122BAB206021)supported by the Natural Science Foundation of Jiangxi Province,ChinaProject(20122BCB23001)supported by the Jiangxi Province Young Scientists Cultivating Programs,China
文摘A mechanical vibration technique to refine solidified microstructure was reported. Vibration energy was directly introduced into a molten alloy by a vibrating horn, and the vibrating horn was melted during vibration. Effects of vibration acceleration and mass ratio on the microstructure of Al-5% Cu alloy were investigated. Results show that the present mechanical vibration could provide localized cooling by extracting heat from the interior of molten alloy, and the cooling rate is strongly dependent on vibration acceleration. It is difficult to refine the solidified microstructure when the treated alloy keeps full liquid state within the entire vibrating duration. Significantly refined microstructure was obtained by applying mechanical vibration during the initial stage of solidification. Moreover, mechanisms of grain refinement were discussed.
文摘MEMS gyroscope is a new inertial navigation sensor,which can measure the input angular rate of sensitive axis using Coriolis effect.Compared to the conventional gyroscope,it owns many unique advantages.A novel structure of vibrating ring gyroscope is proposed and the finite element model of the oscillator is established based on MEMS technology.Through the modal analysis,the natural frequency and mode shapes of the oscillator are obtained.By analyzing the effects of the structural parameters on the mode shapes and frequency of the harmonic oscillator,the optimal design parameters are got.The frequency difference between the operating mode and the other modes is greater than 1kHz after optimization,which can avoid the frequency coupling of the operating mode and other vibrating modes of the oscillator.The simulation results show that the performance parameters of the ring structure meet the design requirements and have obvious advantages.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 50535010 and 10702014)the Project of Liaoning Province Science (Grant No. 2008S095)the National High Technology Research and Development Program of China(Grant No. 2007AA04Z442)
文摘We derive the non-dimensional coupling equation of two exciters, including inertia coupling, stiffness coupling and load coupling. The concept of general dynamic symmetry is proposed to physically explain the synehronisation of the two exciters, which stems from the load coupling that produces the torque of general dynamic symmetry to force the phase difference between the two exciters close to the angle of general dynamic symmetry. The condition of implementing synchronisation is that the torque of general dynamic symmetry is greater than the asymmetric torque of the two motors. A general Lyapunov function is constructed to derive the stability condition of synchronisation that the non-dimensional inertia coupling matrix is positive definite and all its elements are positive. Numeric results show that the structure of the vibrating system can guarantee the stability of synchronisation of the two exciters, and that the greater the distances between the installation positions of the two exciters and the mass centre of the vibrating system are, the stronger the ability of general dynamic symmetry is.
