A class of modified parallel combined methods of real-time numerical simulation are presented for a stiff dynamic system. By combining the parallelism across the system with the parallelism across the method, and rela...A class of modified parallel combined methods of real-time numerical simulation are presented for a stiff dynamic system. By combining the parallelism across the system with the parallelism across the method, and relaxing the dependence of stage value computation on sampling time of input function, a class of modified real-time parallel combined methods are constructed. Stiff and nonstiff subsystems are solved in parallel on a parallel computer by a parallel Rosen-brock method and a parallel RK method, respectively. Their order conditions and convergences are discussed. The numerical simulation experiments show that this class of modified algorithms can get high speed and efficiency.展开更多
In this paper, Differential Transform Method (DTM) is proposed for the closed form solution of linear and non-linear stiff systems. First, we apply DTM to find the series solution which can be easily converted into ex...In this paper, Differential Transform Method (DTM) is proposed for the closed form solution of linear and non-linear stiff systems. First, we apply DTM to find the series solution which can be easily converted into exact solution. The method is described and illustrated with different examples and figures are plotted accordingly. The obtained result confirm that DTM is very easy, effective and convenient.展开更多
The Filon-type quadrature is efficient for highly oscillatory functions - Fourier transforms. Based on Cox and Matthews' ETD schemes, the higher order single step exponential time differencing schemes are presente...The Filon-type quadrature is efficient for highly oscillatory functions - Fourier transforms. Based on Cox and Matthews' ETD schemes, the higher order single step exponential time differencing schemes are presented based on the Filon-type integration and the A-stability of the two-order Adams-Bashforth exponential time differencing scheme is considered. The effectiveness and accuracy of the schemes is tested.展开更多
This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpola...This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpolation and collocation of polynomial approximate solution. The results of this paper bring some useful information. The constructed methods are A-stable up to order 8. As it is shown in the numerical examples, the new methods are superior for stiff systems.展开更多
Background:Due to its high relevance in sports and rehabilitation,the exploration of interventions to further optimize flexibility becomes paramount.While stretching might be the most common way to enhance range of mo...Background:Due to its high relevance in sports and rehabilitation,the exploration of interventions to further optimize flexibility becomes paramount.While stretching might be the most common way to enhance range of motion,these increases could be optimized by imposing an additional activation of the muscle,such as mechanical vibratory stimulation.While several original articles provide promising findings,contradictory results on flexibility and underlying mechanisms(e.g.,stiffness),reasonable effect size(ES)pooling remains scarce.With this work we systematically reviewed the available literature to explore the possibility of potentiating flexibility,stiffness,and passive torque adaptations by superimposing mechanical vibration stimulation.Methods:A systematic search of 4 databases(Web of Science,MEDLINE,Scopus,and Cochrane Public Library)was conducted until December2023 to identify studies comparing mechanical vibratory interventions with passive controls or the same intervention without vibration(sham)on range of motion and passive muscle stiffness in acute(immediate effects after single session)and chronic conditions(multiple sessions over a period of time).ES pooling was conducted using robust variance estimation via R to account for multiple study outcomes.Potential moderators of effects were analyzed using meta regression.Results:Overall,65 studies(acute:1162 participants,chronic:788 participants)were included.There was moderate certainty of evidence for acute flexibility(ES=0.71,p<0.001)and stiffness(ES=-0.89,p=0.006)effects of mechanical vibration treatments vs.passive controls without meaningful results against the sham condition(flexibility:ES=0.20,p<0.001;stiffness:ES=-0.19,p=0.076).Similarly,moderate certainty of evidence was found for chronic vibration effects on flexibility(control:ES=0.64,p=0.043;sham:ES=0.65,p<0.001).Lack of studies and large outcome heterogeneity prevented ES pooling for underlying mechanisms.Conclusion:Vibration improved flexibility in acute and chronic interventions compared to the stand-alone intervention,which can possibly be attributed to an accumulated mechanical stimulus through vibration.However,studies on biological mechanisms are needed to explain flexibility and stiffness effects in response to specific vibration modalities and timing.展开更多
According to the H_(∞)principle,the dynamical performance optimization of a quasi-zero-stiffness(QZS)isolation system with an additional tuned viscous inerter damper(TVID)is studied by using analytical method.The app...According to the H_(∞)principle,the dynamical performance optimization of a quasi-zero-stiffness(QZS)isolation system with an additional tuned viscous inerter damper(TVID)is studied by using analytical method.The approximate analytical solutions of the QZS system coupled with TVID are solved by using the complexification-averaging method,and the expression of stability conditions for steady-state solutions is derived based on Lyapunov method and Routh-Hurwitz criterion.Based on the fixed-point theory,considering the nonlinear stiffness and weak damping of the primary system,the stiffness and damping ratios of TVID coupled to QZS system are optimized by using the equal-peak method.The detailed analysis is conducted on the impact of TVID parameters and their corresponding optimization parameters on the dynamic behavior of the QZS primary system,including saddle-node(SN)bifurcation,Hopf bifurcation,backbone curve of amplitude-frequency response,and force transmissibility.According to the analysis,it is found that the steady-state motion of the system can enter quasi-periodic motion or even chaotic motion after losing stability through Hopf bifurcation.By optimizing the parameters of TVID,the number of SN bifurcation regions of the QZS main system can be reduced from 2 to 1,the Hopf bifurcation region can be eliminated,and the number of branches of backbone curve can be reduced from 2 to 1,thereby improving the dynamical performance of the QZS system.展开更多
The variation of the nonlinear contact stiffness induced by the elastic wheel-holding effect between the aircraft and tractor has an important effect on the vibration characteristics of an airfield towbarless traction...The variation of the nonlinear contact stiffness induced by the elastic wheel-holding effect between the aircraft and tractor has an important effect on the vibration characteristics of an airfield towbarless traction system,making it essential for ensuring the safety of this emerging towing-out mode.In this paper,the frequency evolutionary tendency of the traction system is studied and obtained considering the variation of nonlinear contact stiffness for the first time.A novel modal analysis method,based on a derived nonlinear contact relationship,is proposed to investigate the vibration characteristics for mechanical system.Frequency veering and mode exchange phenomena in the low-order modes are observed due to the variation of nonlinear contact stiffness.These findings are further validated by the experimental results of a scaled-down model.In addition,it is also found that the veering critical point will be shifted with the external loads.The study provides valuable insights into the vibration characteristics and frequency veering behavior of similar mechanism-based systems,such as towbarless traction system,and has important implications for improving their design and operational performance.展开更多
Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,where the resulting nonlinearities critically influence subh...Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,where the resulting nonlinearities critically influence subharmonic resonance phenomena,yet comprehensive investigations remain limited.This study employs the generalized harmonic balance(HB)method to conduct an analytical investigation of the subharmonic resonance behavior in asymmetric stiffness nonlinear systems with time delay.To further examine the switching behavior between primary and subharmonic resonances,a numerical continuation approach combining the shooting method and the parameter continuation algorithm is developed.The analytical and numerical continuation solutions are validated through direct numerical integration.Subsequently,the switching behavior and associated bifurcation points are analyzed by means of the numerical continuation results in conjunction with the Floquet theory.Finally,the effects of delay parameters on the existence range of subharmonic responses are discussed in detail,and the influence of initial conditions on system dynamics is explored with basin of attraction plots.This work establishes a comprehensive framework for the analytical and numerical study on time-delayed nonlinear systems with asymmetric stiffness,providing valuable theoretical insights into the stability management of such dynamic systems.展开更多
BACKGROUND The impact of transjugular intrahepatic portosystemic shunt(TIPS)on liver and spleen stiffness remains unclear,as does the association between preoperative liver and spleen stiffness and prognosis following...BACKGROUND The impact of transjugular intrahepatic portosystemic shunt(TIPS)on liver and spleen stiffness remains unclear,as does the association between preoperative liver and spleen stiffness and prognosis following TIPS.AIM To investigate changes in liver and spleen stiffness after TIPS and examines the relationship between these parameters and the prognosis of post-TIPS patients.METHODS A total of 76 patients with liver cirrhosis and portal hypertension who underwent TIPS were included.Liver and spleen stiffness was assessed using the sound touch quantify(STQ)value,determined via point shear wave elastography in ultrasound imaging.Cox regression analysis was employed to evaluate the relationship between liver and spleen stiffness and cumulative survival in TIPS patients.RESULTS The liver STQ value demonstrated a marginally decreasing trend over time(P=0.052),while the spleen STQ value showed a significantly decreasing trend(P=0.025).Spleen STQ was positively correlated with portal pressure gradient(PPG)levels(rs=0.327,P=0.025).Cox regression analysis indicated that older age[hazard ratio(HR)=1.063,95%CI:0.997-1.133,P=0.060]and a higher liver STQ value(HR=1.051,95%CI:1.009-1.095,P=0.018)were associated with an increased mortality risk after TIPS.No significant correlation was found between liver or spleen stiffness and overt hepatic encephalopathy post-TIPS.The liver STQ value[area under the receiver operating characteristic curve(AUC)=0.724(95%CI:0.563-0.884)]showed superior predictive performance compared to the Child-Pugh score[AUC=0.699(95%CI:0.529-0.870)]and was comparable to the model for end-stage liver disease score[AUC=0.746(95%CI:0.591-0.902)].CONCLUSION Following TIPS,spleen stiffness exhibited a more pronounced change than liver stiffness and was positively associated with PPG.Preoperative liver stiffness serves as a prognostic indicator for survival in patients undergoing TIPS.展开更多
As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road ...As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road conditions,this paper proposes a linear motor active suspension with quasi-zero stiffness(QZS)air spring system.Firstly,a dynamic model of the linear motor active suspension with QZS air spring system is established.Secondly,considering the random uncertainties in the linear motor parameters due to manufacturing and environmental factors,a dynamic model and state equations incorporating these uncertainties are constructed using the polynomial chaos expansion(PCE)method.Then,based on H_(2) robust control theory and the Kalman filter,a state feedback control law is derived,accounting for the random parameter uncertainties.Finally,simulation and hardware-in-the-loop(HIL)experimental results demonstrate that the PCE-H_(2) robust controller not only provides better performance in terms of vehicle ride comfort compared to general H_(2) robust controller but also exhibits higher robustness to the effects of random uncertain parameters,resulting in more stable control performance.展开更多
Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system....Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system.How ever,traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles To address this issue,a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension(GIQZSPS)is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes.This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension.It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers.Firstly,a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system.By the nonlinear mechanical model of GIQZSPS system,the force transmissibility rate is chosen as the evaluation index to analyze characteristics.Furthermore,a testing bench simulating 1/4 GIQZSPS system is designed,and the testing analysis of the model validation and isolating performance is carried out.The results show that compared to traditional pneumatic suspension,the GIQZSPS designed in the article has a lower natural frequency.And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.展开更多
The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This s...The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.展开更多
Increased matrix stiffness of nucleus pulposus(NP)tissue is a main feature of intervertebral disc degeneration(IVDD)and affects various functions of nucleus pulposus cells(NPCs).Glycolysis is the main energy source fo...Increased matrix stiffness of nucleus pulposus(NP)tissue is a main feature of intervertebral disc degeneration(IVDD)and affects various functions of nucleus pulposus cells(NPCs).Glycolysis is the main energy source for NPC survival,but the effects and underlying mechanisms of increased extracellular matrix(ECM)stiffness on NPC glycolysis remain unknown.In this study,hydrogels with different stiffness were established to mimic the mechanical environment of NPCs.Notably,increased matrix stiffness in degenerated NP tissues from IVDD patients was accompanied with impaired glycolysis,and NPCs cultured on rigid substrates exhibited a reduction in glycolysis.展开更多
A conceptual model of intermittent joints is introduced to the cyclic shear test in the laboratory to explore the effects of loading parameters on its shear behavior under cyclic shear loading.The results show that th...A conceptual model of intermittent joints is introduced to the cyclic shear test in the laboratory to explore the effects of loading parameters on its shear behavior under cyclic shear loading.The results show that the loading parameters(initial normal stress,normal stiffness,and shear velocity)determine propagation paths of the wing and secondary cracks in rock bridges during the initial shear cycle,creating different morphologies of macroscopic step-path rupture surfaces and asperities on them.The differences in stress state and rupture surface induce different cyclic shear responses.It shows that high initial normal stress accelerates asperity degradation,raises shear resistance,and promotes compression of intermittent joints.In addition,high normal stiffness provides higher normal stress and shear resistance during the initial cycles and inhibits the dilation and compression of intermittent joints.High shear velocity results in a higher shear resistance,greater dilation,and greater compression.Finally,shear strength is most sensitive to initial normal stress,followed by shear velocity and normal stiffness.Moreover,average dilation angle is most sensitive to initial normal stress,followed by normal stiffness and shear velocity.During the shear cycles,frictional coefficient is affected by asperity degradation,backfilling of rock debris,and frictional area,exhibiting a non-monotonic behavior.展开更多
Neuronal growth, extension, branching, and formation of neural networks are markedly influenced by the extracellular matrix—a complex network composed of proteins and carbohydrates secreted by cells. In addition to p...Neuronal growth, extension, branching, and formation of neural networks are markedly influenced by the extracellular matrix—a complex network composed of proteins and carbohydrates secreted by cells. In addition to providing physical support for cells, the extracellular matrix also conveys critical mechanical stiffness cues. During the development of the nervous system, extracellular matrix stiffness plays a central role in guiding neuronal growth, particularly in the context of axonal extension, which is crucial for the formation of neural networks. In neural tissue engineering, manipulation of biomaterial stiffness is a promising strategy to provide a permissive environment for the repair and regeneration of injured nervous tissue. Recent research has fine-tuned synthetic biomaterials to fabricate scaffolds that closely replicate the stiffness profiles observed in the nervous system. In this review, we highlight the molecular mechanisms by which extracellular matrix stiffness regulates axonal growth and regeneration. We highlight the progress made in the development of stiffness-tunable biomaterials to emulate in vivo extracellular matrix environments, with an emphasis on their application in neural repair and regeneration, along with a discussion of the current limitations and future prospects. The exploration and optimization of the stiffness-tunable biomaterials has the potential to markedly advance the development of neural tissue engineering.展开更多
Railways are very important to our society due to their efficiency and reduced environmental effects.A system for the measurement of the condition of the formation on which a permanent way(pairs of rails laid on sleep...Railways are very important to our society due to their efficiency and reduced environmental effects.A system for the measurement of the condition of the formation on which a permanent way(pairs of rails laid on sleepers)is located is investigated in this work.This will allow effective asset management and reduce the costs of rail maintenance.Areas where the formation is either weak or changes rapidly present problems when maintaining a section of the track due to poor track geometry.Formation stiffness is a difficult parameter to measure and requires extensive research efforts.In this work a train-track interaction problem is investigated with a quarter train track model,which consists of a coach,bogie and wheel.The train-irregularity model is developed which computes the train response to irregularities,such as the deflection by stiffness changes.Using this train–irregularity model,the effects of train speed on the wheel/rail interaction force over the stiffness changes are studied and the track stiffness is also analysed,which will be used in future analysis to calculate the actual stiffness of the track when using laser measurement techniques.展开更多
Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design o...Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design optimization of variable stiffness of fiber-reinforced composite laminates has attracted widespread attention from scholars and industry. In these aerospace composite structures, numerous cutout panels and shells serve as access points for maintaining electrical, fuel, and hydraulic systems. The traditional fiber-reinforced composite laminate subtractive drilling manufacturing inevitably faces the problems of interlayer delamination, fiber fracture, and burr of the laminate. Continuous fiber additive manufacturing technology offers the potential for integrated design optimization and manufacturing with high structural performance. Considering the integration of design and manufacturability in continuous fiber additive manufacturing, the paper proposes linear and nonlinear filtering strategies based on the Normal Distribution Fiber Optimization (NDFO) material interpolation scheme to overcome the challenge of discrete fiber optimization results, which are difficult to apply directly to continuous fiber additive manufacturing. With minimizing structural compliance as the objective function, the proposed approach provides a strategy to achieve continuity of discrete fiber paths in the variable stiffness design optimization of composite laminates with regular and irregular holes. In the variable stiffness design optimization model, the number of candidate fiber laying angles in the NDFO material interpolation scheme is considered as design variable. The sensitivity information of structural compliance with respect to the number of candidate fiber laying angles is obtained using the analytical sensitivity analysis method. Based on the proposed variable stiffness design optimization method for complex perforated composite laminates, the numerical examples consider the variable stiffness design optimization of typical non-perforated and perforated composite laminates with circular, square, and irregular holes, and systematically discuss the number of candidate discrete fiber laying angles, discrete fiber continuous filtering strategies, and filter radius on structural compliance, continuity, and manufacturability. The optimized discrete fiber angles of variable stiffness laminates are converted into continuous fiber laying paths using a streamlined process for continuous fiber additive manufacturing. Meanwhile, the optimized non-perforated and perforated MBB beams after discrete fiber continuous treatment, are manufactured using continuous fiber co-extrusion additive manufacturing technology to verify the effectiveness of the variable stiffness fiber optimization framework proposed in this paper.展开更多
BACKGROUND Clinically significant portal hypertension(CSPH)is a crucial prognostic deter-minant for liver-related events(LREs)in patients with compensated viral cir-rhosis.Liver stiffness measurement(LSM)-related mark...BACKGROUND Clinically significant portal hypertension(CSPH)is a crucial prognostic deter-minant for liver-related events(LREs)in patients with compensated viral cir-rhosis.Liver stiffness measurement(LSM)-related markers may help to predict the risk of LREs.AIM To evaluate the value of LSM and its composite biomarkers[LSM-platelet ratio(LPR),LSM-albumin ratio(LAR)]in predicting LREs.METHODS This study retrospectively enrolled compensated viral cirrhosis patients with CSPH.The Cox regression model was employed to examine the prediction of LSM,LPR,and LAR for LREs.The model performance was assessed through receiver operating characteristic,decision curve,and time-dependent area under the curve analysis.The Kaplan-Meier curve was used to evaluate the cumulative incidence of LREs,and further stratified analysis of different LREs was per-formed.RESULTS A total of 598 patients were included,and 319 patients(53.3%)developed LREs during follow-up.Multivariate proportional hazards modeling demonstrated that LSM,LPR,and LAR were independent predictors of LREs.LPR had better performance in predicting LREs than LAR and LSM(area under the curve=0.780,0.727,0.683,respectively,all P<0.05).The cumulative incidence of LREs in the high-risk group were significantly higher than that in the low-risk group(P<0.001).Among the different LREs,LPR was superior to LSM and LAR in predicting liver decompensation,while the difference in predicting hepatocellular carcinoma and liver-related death was relatively small.CONCLUSION LPR is superior to LSM and LAR in predicting LREs in compensated viral cirrhosis patients with CSPH,especially in predicting liver decompensation.展开更多
Quasi-zero stiffness(QZS)isolators have received considerable attention over the past years due to their outstanding vibration isolation performance in low-frequency bands.However,traditional mechanisms for achieving ...Quasi-zero stiffness(QZS)isolators have received considerable attention over the past years due to their outstanding vibration isolation performance in low-frequency bands.However,traditional mechanisms for achieving QZS suffer from low stiffness regions and significant nonlinear restoring forces with hardening characteristics,often struggling to withstand excitations with high amplitude.This paper presents a novel QZS vibration isolator that utilizes a more compact spring-rod mechanism(SRM)to provide primary negative stiffness.The nonlinearity of SRM is adjustable via altering the raceway of its spring-rod end,along with the compensatory force provided by the cam-roller mechanism so as to avoid complex nonlinear behaviors.The absolute zero stiffness can be achieved by a well-designed raceway curve with a concise mathematical expression.The nonlinear stiffness with softening properties can also be achieved by parameter adjustment.The study begins with the forcedisplacement relationship of the integrated mechanism first,followed by the design theory of the cam profile.The dynamic response and absolute displacement transmissibility of the isolation system are obtained based on the harmonic balance method.The experimental results show that the proposed vibration isolator maintains relatively low-dynamic stiffness even under non-ideal conditions,and exhibits enhanced vibration isolation performance compared to the corresponding linear isolator.展开更多
The deterioration of soft rocks caused by freeze-thaw(F-T)climatic cycles results in huge structural and financial loss for foundation systems placed on soft rocks prone to F-T actions.In this study,cementtreated sand...The deterioration of soft rocks caused by freeze-thaw(F-T)climatic cycles results in huge structural and financial loss for foundation systems placed on soft rocks prone to F-T actions.In this study,cementtreated sand(CTS)and natural soft shale were subjected to unconfined compression and splitting tensile strength tests for evaluation of unconfined compressive strength(UCS,qu),initial small-strain Young’s modulus(Eo)using linear displacement transducers(LDT)up to a small strain of 0.001%,and secant elastic modulus(E_(50))using linear variable differential transducers(LVDTs)up to a large strain of 6%before and after reproduced laboratory weathering(RLW)cycles(-20℃e-110℃).The results showed that eight F-T cycles caused a reduction in q_(u),E_(50) and E_(o),which was 8.6,15.1,and 14.5 times for the CTS,and 2.2,3.5,and 5.3 times for the natural shale,respectively.The tensile strength of the CTS and natural rock samples exhibited a degradation of 5.4 times(after the 8th RLW cycle)and 2.7 times(after the 15th RLW cycle),respectively.Novel correlations have been developed to predict Eo(response)from the parameters qu and E_(50)(predictors)using MATLAB software's curve fitter.The findings of this study will assist in the design of foundations in soft rocks subjected to freezing and thawing.The analysis of variance(ANOVA)indicated 95%confidence in data health for the design of retaining walls,building foundations,excavation in soft rock,large-diameter borehole stability,and transportation tunnels in rocks for an operational strain range of 0.1%e0.01%(using LVDT)and a reference strain of less than 0.001%(using LDT).展开更多
基金This project was supported by the National Natural Science Foundation of China (19871080).
文摘A class of modified parallel combined methods of real-time numerical simulation are presented for a stiff dynamic system. By combining the parallelism across the system with the parallelism across the method, and relaxing the dependence of stage value computation on sampling time of input function, a class of modified real-time parallel combined methods are constructed. Stiff and nonstiff subsystems are solved in parallel on a parallel computer by a parallel Rosen-brock method and a parallel RK method, respectively. Their order conditions and convergences are discussed. The numerical simulation experiments show that this class of modified algorithms can get high speed and efficiency.
文摘In this paper, Differential Transform Method (DTM) is proposed for the closed form solution of linear and non-linear stiff systems. First, we apply DTM to find the series solution which can be easily converted into exact solution. The method is described and illustrated with different examples and figures are plotted accordingly. The obtained result confirm that DTM is very easy, effective and convenient.
基金Projects(02JJY2006, 03JJY2001) supported by Natural Science Foundation of Hunan Province project supported by JSPS Fellowship Research Program
文摘The Filon-type quadrature is efficient for highly oscillatory functions - Fourier transforms. Based on Cox and Matthews' ETD schemes, the higher order single step exponential time differencing schemes are presented based on the Filon-type integration and the A-stability of the two-order Adams-Bashforth exponential time differencing scheme is considered. The effectiveness and accuracy of the schemes is tested.
文摘This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpolation and collocation of polynomial approximate solution. The results of this paper bring some useful information. The constructed methods are A-stable up to order 8. As it is shown in the numerical examples, the new methods are superior for stiff systems.
文摘Background:Due to its high relevance in sports and rehabilitation,the exploration of interventions to further optimize flexibility becomes paramount.While stretching might be the most common way to enhance range of motion,these increases could be optimized by imposing an additional activation of the muscle,such as mechanical vibratory stimulation.While several original articles provide promising findings,contradictory results on flexibility and underlying mechanisms(e.g.,stiffness),reasonable effect size(ES)pooling remains scarce.With this work we systematically reviewed the available literature to explore the possibility of potentiating flexibility,stiffness,and passive torque adaptations by superimposing mechanical vibration stimulation.Methods:A systematic search of 4 databases(Web of Science,MEDLINE,Scopus,and Cochrane Public Library)was conducted until December2023 to identify studies comparing mechanical vibratory interventions with passive controls or the same intervention without vibration(sham)on range of motion and passive muscle stiffness in acute(immediate effects after single session)and chronic conditions(multiple sessions over a period of time).ES pooling was conducted using robust variance estimation via R to account for multiple study outcomes.Potential moderators of effects were analyzed using meta regression.Results:Overall,65 studies(acute:1162 participants,chronic:788 participants)were included.There was moderate certainty of evidence for acute flexibility(ES=0.71,p<0.001)and stiffness(ES=-0.89,p=0.006)effects of mechanical vibration treatments vs.passive controls without meaningful results against the sham condition(flexibility:ES=0.20,p<0.001;stiffness:ES=-0.19,p=0.076).Similarly,moderate certainty of evidence was found for chronic vibration effects on flexibility(control:ES=0.64,p=0.043;sham:ES=0.65,p<0.001).Lack of studies and large outcome heterogeneity prevented ES pooling for underlying mechanisms.Conclusion:Vibration improved flexibility in acute and chronic interventions compared to the stand-alone intervention,which can possibly be attributed to an accumulated mechanical stimulus through vibration.However,studies on biological mechanisms are needed to explain flexibility and stiffness effects in response to specific vibration modalities and timing.
基金supported by the National Natural Science Foundation of China(Grant Nos.12272241,12202286,and U1934201)Natural Science Foundation of Hebei Province(Grant Nos.A2021210012 and A2024210041).
文摘According to the H_(∞)principle,the dynamical performance optimization of a quasi-zero-stiffness(QZS)isolation system with an additional tuned viscous inerter damper(TVID)is studied by using analytical method.The approximate analytical solutions of the QZS system coupled with TVID are solved by using the complexification-averaging method,and the expression of stability conditions for steady-state solutions is derived based on Lyapunov method and Routh-Hurwitz criterion.Based on the fixed-point theory,considering the nonlinear stiffness and weak damping of the primary system,the stiffness and damping ratios of TVID coupled to QZS system are optimized by using the equal-peak method.The detailed analysis is conducted on the impact of TVID parameters and their corresponding optimization parameters on the dynamic behavior of the QZS primary system,including saddle-node(SN)bifurcation,Hopf bifurcation,backbone curve of amplitude-frequency response,and force transmissibility.According to the analysis,it is found that the steady-state motion of the system can enter quasi-periodic motion or even chaotic motion after losing stability through Hopf bifurcation.By optimizing the parameters of TVID,the number of SN bifurcation regions of the QZS main system can be reduced from 2 to 1,the Hopf bifurcation region can be eliminated,and the number of branches of backbone curve can be reduced from 2 to 1,thereby improving the dynamical performance of the QZS system.
基金co-supported by the Key Projects of the Civil Aviation Joint Fund of the National Natural Science Foundation of China(No.U2033208)。
文摘The variation of the nonlinear contact stiffness induced by the elastic wheel-holding effect between the aircraft and tractor has an important effect on the vibration characteristics of an airfield towbarless traction system,making it essential for ensuring the safety of this emerging towing-out mode.In this paper,the frequency evolutionary tendency of the traction system is studied and obtained considering the variation of nonlinear contact stiffness for the first time.A novel modal analysis method,based on a derived nonlinear contact relationship,is proposed to investigate the vibration characteristics for mechanical system.Frequency veering and mode exchange phenomena in the low-order modes are observed due to the variation of nonlinear contact stiffness.These findings are further validated by the experimental results of a scaled-down model.In addition,it is also found that the veering critical point will be shifted with the external loads.The study provides valuable insights into the vibration characteristics and frequency veering behavior of similar mechanism-based systems,such as towbarless traction system,and has important implications for improving their design and operational performance.
基金Project supported by the National Natural Science Foundation of China(Nos.U24B2062,520754285247051087)+1 种基金the Two-chain Fusion High-end Machine Tool Project of Shaanxi Province of China(No.2021LLRh-01-02)the Youth Fund of the National Natural Science Foundation of China(No.52205281)。
文摘Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,where the resulting nonlinearities critically influence subharmonic resonance phenomena,yet comprehensive investigations remain limited.This study employs the generalized harmonic balance(HB)method to conduct an analytical investigation of the subharmonic resonance behavior in asymmetric stiffness nonlinear systems with time delay.To further examine the switching behavior between primary and subharmonic resonances,a numerical continuation approach combining the shooting method and the parameter continuation algorithm is developed.The analytical and numerical continuation solutions are validated through direct numerical integration.Subsequently,the switching behavior and associated bifurcation points are analyzed by means of the numerical continuation results in conjunction with the Floquet theory.Finally,the effects of delay parameters on the existence range of subharmonic responses are discussed in detail,and the influence of initial conditions on system dynamics is explored with basin of attraction plots.This work establishes a comprehensive framework for the analytical and numerical study on time-delayed nonlinear systems with asymmetric stiffness,providing valuable theoretical insights into the stability management of such dynamic systems.
基金Supported by National Natural Science Foundation of China,No.82200650Shanxi Provincial Clinical Research Center for Interventional Medicine,No.202204010501004+3 种基金the Precision Interventional Diagnosis and Treatment Technology Innovation Base for Cirrhosis and Portal Hypertension,No.YDZJSX20231B010the Natural Science Foundation of Shanxi Province,No.20210302124282 and No.202203021212046the Shanxi Province Higher Education“Billion Project Science and Technology Guidance Project”,No.2C622024120the National Natural Science Foundation of China Supporting Fund,No.Y82200650.
文摘BACKGROUND The impact of transjugular intrahepatic portosystemic shunt(TIPS)on liver and spleen stiffness remains unclear,as does the association between preoperative liver and spleen stiffness and prognosis following TIPS.AIM To investigate changes in liver and spleen stiffness after TIPS and examines the relationship between these parameters and the prognosis of post-TIPS patients.METHODS A total of 76 patients with liver cirrhosis and portal hypertension who underwent TIPS were included.Liver and spleen stiffness was assessed using the sound touch quantify(STQ)value,determined via point shear wave elastography in ultrasound imaging.Cox regression analysis was employed to evaluate the relationship between liver and spleen stiffness and cumulative survival in TIPS patients.RESULTS The liver STQ value demonstrated a marginally decreasing trend over time(P=0.052),while the spleen STQ value showed a significantly decreasing trend(P=0.025).Spleen STQ was positively correlated with portal pressure gradient(PPG)levels(rs=0.327,P=0.025).Cox regression analysis indicated that older age[hazard ratio(HR)=1.063,95%CI:0.997-1.133,P=0.060]and a higher liver STQ value(HR=1.051,95%CI:1.009-1.095,P=0.018)were associated with an increased mortality risk after TIPS.No significant correlation was found between liver or spleen stiffness and overt hepatic encephalopathy post-TIPS.The liver STQ value[area under the receiver operating characteristic curve(AUC)=0.724(95%CI:0.563-0.884)]showed superior predictive performance compared to the Child-Pugh score[AUC=0.699(95%CI:0.529-0.870)]and was comparable to the model for end-stage liver disease score[AUC=0.746(95%CI:0.591-0.902)].CONCLUSION Following TIPS,spleen stiffness exhibited a more pronounced change than liver stiffness and was positively associated with PPG.Preoperative liver stiffness serves as a prognostic indicator for survival in patients undergoing TIPS.
基金Supported by National Natural Science Foundation of China(Grant No.51875256)Open Platform Fund of Human Institute of Technology(Grant No.KFA22009).
文摘As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road conditions,this paper proposes a linear motor active suspension with quasi-zero stiffness(QZS)air spring system.Firstly,a dynamic model of the linear motor active suspension with QZS air spring system is established.Secondly,considering the random uncertainties in the linear motor parameters due to manufacturing and environmental factors,a dynamic model and state equations incorporating these uncertainties are constructed using the polynomial chaos expansion(PCE)method.Then,based on H_(2) robust control theory and the Kalman filter,a state feedback control law is derived,accounting for the random parameter uncertainties.Finally,simulation and hardware-in-the-loop(HIL)experimental results demonstrate that the PCE-H_(2) robust controller not only provides better performance in terms of vehicle ride comfort compared to general H_(2) robust controller but also exhibits higher robustness to the effects of random uncertain parameters,resulting in more stable control performance.
基金Supported by National Natural Science Foundation of China (Grant No.51875256)Open Platform Fund of Human Institute of Technology (Grant No.KFA22009)。
文摘Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system.How ever,traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles To address this issue,a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension(GIQZSPS)is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes.This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension.It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers.Firstly,a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system.By the nonlinear mechanical model of GIQZSPS system,the force transmissibility rate is chosen as the evaluation index to analyze characteristics.Furthermore,a testing bench simulating 1/4 GIQZSPS system is designed,and the testing analysis of the model validation and isolating performance is carried out.The results show that compared to traditional pneumatic suspension,the GIQZSPS designed in the article has a lower natural frequency.And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.
基金Supported by National Natural Science Foundation of China (Grant No.52275036)Key Research and Development Project of the Jiaxing Science and Technology Bureau (Grant No.2022BZ10004)。
文摘The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.
基金supported by the National Nature Science Foundation of China(No.82002345 to J.D and 81902179 to L.S)the Gusu Talent Program(No.Qngg2022008 and GSWS2021027 to J.D)the Preliminary Research Project of the Second Affiliated Hospital of Soochow University(No.SDFEYBS1905 to J.D).
文摘Increased matrix stiffness of nucleus pulposus(NP)tissue is a main feature of intervertebral disc degeneration(IVDD)and affects various functions of nucleus pulposus cells(NPCs).Glycolysis is the main energy source for NPC survival,but the effects and underlying mechanisms of increased extracellular matrix(ECM)stiffness on NPC glycolysis remain unknown.In this study,hydrogels with different stiffness were established to mimic the mechanical environment of NPCs.Notably,increased matrix stiffness in degenerated NP tissues from IVDD patients was accompanied with impaired glycolysis,and NPCs cultured on rigid substrates exhibited a reduction in glycolysis.
基金financially supported by the National Natural Science Foundation of China(Grant No.42172292)Taishan Scholars Project Special Funding,and Shandong Energy Group(Grant No.SNKJ 2022A01-R26).
文摘A conceptual model of intermittent joints is introduced to the cyclic shear test in the laboratory to explore the effects of loading parameters on its shear behavior under cyclic shear loading.The results show that the loading parameters(initial normal stress,normal stiffness,and shear velocity)determine propagation paths of the wing and secondary cracks in rock bridges during the initial shear cycle,creating different morphologies of macroscopic step-path rupture surfaces and asperities on them.The differences in stress state and rupture surface induce different cyclic shear responses.It shows that high initial normal stress accelerates asperity degradation,raises shear resistance,and promotes compression of intermittent joints.In addition,high normal stiffness provides higher normal stress and shear resistance during the initial cycles and inhibits the dilation and compression of intermittent joints.High shear velocity results in a higher shear resistance,greater dilation,and greater compression.Finally,shear strength is most sensitive to initial normal stress,followed by shear velocity and normal stiffness.Moreover,average dilation angle is most sensitive to initial normal stress,followed by normal stiffness and shear velocity.During the shear cycles,frictional coefficient is affected by asperity degradation,backfilling of rock debris,and frictional area,exhibiting a non-monotonic behavior.
基金supported by the Natio`nal Natural Science Foundation of China,No. 81801241a grant from Sichuan Science and Technology Program,No. 2023NSFSC1578Scientific Research Projects of Southwest Medical University,No. 2022ZD002 (all to JX)。
文摘Neuronal growth, extension, branching, and formation of neural networks are markedly influenced by the extracellular matrix—a complex network composed of proteins and carbohydrates secreted by cells. In addition to providing physical support for cells, the extracellular matrix also conveys critical mechanical stiffness cues. During the development of the nervous system, extracellular matrix stiffness plays a central role in guiding neuronal growth, particularly in the context of axonal extension, which is crucial for the formation of neural networks. In neural tissue engineering, manipulation of biomaterial stiffness is a promising strategy to provide a permissive environment for the repair and regeneration of injured nervous tissue. Recent research has fine-tuned synthetic biomaterials to fabricate scaffolds that closely replicate the stiffness profiles observed in the nervous system. In this review, we highlight the molecular mechanisms by which extracellular matrix stiffness regulates axonal growth and regeneration. We highlight the progress made in the development of stiffness-tunable biomaterials to emulate in vivo extracellular matrix environments, with an emphasis on their application in neural repair and regeneration, along with a discussion of the current limitations and future prospects. The exploration and optimization of the stiffness-tunable biomaterials has the potential to markedly advance the development of neural tissue engineering.
文摘Railways are very important to our society due to their efficiency and reduced environmental effects.A system for the measurement of the condition of the formation on which a permanent way(pairs of rails laid on sleepers)is located is investigated in this work.This will allow effective asset management and reduce the costs of rail maintenance.Areas where the formation is either weak or changes rapidly present problems when maintaining a section of the track due to poor track geometry.Formation stiffness is a difficult parameter to measure and requires extensive research efforts.In this work a train-track interaction problem is investigated with a quarter train track model,which consists of a coach,bogie and wheel.The train-irregularity model is developed which computes the train response to irregularities,such as the deflection by stiffness changes.Using this train–irregularity model,the effects of train speed on the wheel/rail interaction force over the stiffness changes are studied and the track stiffness is also analysed,which will be used in future analysis to calculate the actual stiffness of the track when using laser measurement techniques.
基金supports for this research were provided by the National Natural Science Foundation of China(No.12272301,12002278,U1906233)the Guangdong Basic and Applied Basic Research Foundation,China(Nos.2023A1515011970,2024A1515010256)+1 种基金the Dalian City Supports Innovation and Entrepreneurship Projects for High-Level Talents,China(2021RD16)the Key R&D Project of CSCEC,China(No.CSCEC-2020-Z-4).
文摘Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design optimization of variable stiffness of fiber-reinforced composite laminates has attracted widespread attention from scholars and industry. In these aerospace composite structures, numerous cutout panels and shells serve as access points for maintaining electrical, fuel, and hydraulic systems. The traditional fiber-reinforced composite laminate subtractive drilling manufacturing inevitably faces the problems of interlayer delamination, fiber fracture, and burr of the laminate. Continuous fiber additive manufacturing technology offers the potential for integrated design optimization and manufacturing with high structural performance. Considering the integration of design and manufacturability in continuous fiber additive manufacturing, the paper proposes linear and nonlinear filtering strategies based on the Normal Distribution Fiber Optimization (NDFO) material interpolation scheme to overcome the challenge of discrete fiber optimization results, which are difficult to apply directly to continuous fiber additive manufacturing. With minimizing structural compliance as the objective function, the proposed approach provides a strategy to achieve continuity of discrete fiber paths in the variable stiffness design optimization of composite laminates with regular and irregular holes. In the variable stiffness design optimization model, the number of candidate fiber laying angles in the NDFO material interpolation scheme is considered as design variable. The sensitivity information of structural compliance with respect to the number of candidate fiber laying angles is obtained using the analytical sensitivity analysis method. Based on the proposed variable stiffness design optimization method for complex perforated composite laminates, the numerical examples consider the variable stiffness design optimization of typical non-perforated and perforated composite laminates with circular, square, and irregular holes, and systematically discuss the number of candidate discrete fiber laying angles, discrete fiber continuous filtering strategies, and filter radius on structural compliance, continuity, and manufacturability. The optimized discrete fiber angles of variable stiffness laminates are converted into continuous fiber laying paths using a streamlined process for continuous fiber additive manufacturing. Meanwhile, the optimized non-perforated and perforated MBB beams after discrete fiber continuous treatment, are manufactured using continuous fiber co-extrusion additive manufacturing technology to verify the effectiveness of the variable stiffness fiber optimization framework proposed in this paper.
基金Supported by the High-Level Chinese Medicine Key Discipline Construction Project,No.zyyzdxk-2023005Capital’s Funds for Health Improvement and Research,No.2024-1-2173+2 种基金National Natural Science Foundation of China,No.82474419 and No.82474426Beijing Municipal Natural Science Foundation,No.7232272Beijing Traditional Chinese Medicine Technology Development Fund Project,No.BJZYZD-2023-12.
文摘BACKGROUND Clinically significant portal hypertension(CSPH)is a crucial prognostic deter-minant for liver-related events(LREs)in patients with compensated viral cir-rhosis.Liver stiffness measurement(LSM)-related markers may help to predict the risk of LREs.AIM To evaluate the value of LSM and its composite biomarkers[LSM-platelet ratio(LPR),LSM-albumin ratio(LAR)]in predicting LREs.METHODS This study retrospectively enrolled compensated viral cirrhosis patients with CSPH.The Cox regression model was employed to examine the prediction of LSM,LPR,and LAR for LREs.The model performance was assessed through receiver operating characteristic,decision curve,and time-dependent area under the curve analysis.The Kaplan-Meier curve was used to evaluate the cumulative incidence of LREs,and further stratified analysis of different LREs was per-formed.RESULTS A total of 598 patients were included,and 319 patients(53.3%)developed LREs during follow-up.Multivariate proportional hazards modeling demonstrated that LSM,LPR,and LAR were independent predictors of LREs.LPR had better performance in predicting LREs than LAR and LSM(area under the curve=0.780,0.727,0.683,respectively,all P<0.05).The cumulative incidence of LREs in the high-risk group were significantly higher than that in the low-risk group(P<0.001).Among the different LREs,LPR was superior to LSM and LAR in predicting liver decompensation,while the difference in predicting hepatocellular carcinoma and liver-related death was relatively small.CONCLUSION LPR is superior to LSM and LAR in predicting LREs in compensated viral cirrhosis patients with CSPH,especially in predicting liver decompensation.
基金supported by the National Natural Science Foundation of China(Grant No.11732006)the“Qinglan Project”of Jiangsu Higher Education Institutions.
文摘Quasi-zero stiffness(QZS)isolators have received considerable attention over the past years due to their outstanding vibration isolation performance in low-frequency bands.However,traditional mechanisms for achieving QZS suffer from low stiffness regions and significant nonlinear restoring forces with hardening characteristics,often struggling to withstand excitations with high amplitude.This paper presents a novel QZS vibration isolator that utilizes a more compact spring-rod mechanism(SRM)to provide primary negative stiffness.The nonlinearity of SRM is adjustable via altering the raceway of its spring-rod end,along with the compensatory force provided by the cam-roller mechanism so as to avoid complex nonlinear behaviors.The absolute zero stiffness can be achieved by a well-designed raceway curve with a concise mathematical expression.The nonlinear stiffness with softening properties can also be achieved by parameter adjustment.The study begins with the forcedisplacement relationship of the integrated mechanism first,followed by the design theory of the cam profile.The dynamic response and absolute displacement transmissibility of the isolation system are obtained based on the harmonic balance method.The experimental results show that the proposed vibration isolator maintains relatively low-dynamic stiffness even under non-ideal conditions,and exhibits enhanced vibration isolation performance compared to the corresponding linear isolator.
文摘The deterioration of soft rocks caused by freeze-thaw(F-T)climatic cycles results in huge structural and financial loss for foundation systems placed on soft rocks prone to F-T actions.In this study,cementtreated sand(CTS)and natural soft shale were subjected to unconfined compression and splitting tensile strength tests for evaluation of unconfined compressive strength(UCS,qu),initial small-strain Young’s modulus(Eo)using linear displacement transducers(LDT)up to a small strain of 0.001%,and secant elastic modulus(E_(50))using linear variable differential transducers(LVDTs)up to a large strain of 6%before and after reproduced laboratory weathering(RLW)cycles(-20℃e-110℃).The results showed that eight F-T cycles caused a reduction in q_(u),E_(50) and E_(o),which was 8.6,15.1,and 14.5 times for the CTS,and 2.2,3.5,and 5.3 times for the natural shale,respectively.The tensile strength of the CTS and natural rock samples exhibited a degradation of 5.4 times(after the 8th RLW cycle)and 2.7 times(after the 15th RLW cycle),respectively.Novel correlations have been developed to predict Eo(response)from the parameters qu and E_(50)(predictors)using MATLAB software's curve fitter.The findings of this study will assist in the design of foundations in soft rocks subjected to freezing and thawing.The analysis of variance(ANOVA)indicated 95%confidence in data health for the design of retaining walls,building foundations,excavation in soft rock,large-diameter borehole stability,and transportation tunnels in rocks for an operational strain range of 0.1%e0.01%(using LVDT)and a reference strain of less than 0.001%(using LDT).
