Human motion induced vibration has very low frequency,ranging from 2 Hz to 5 Hz.Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the...Human motion induced vibration has very low frequency,ranging from 2 Hz to 5 Hz.Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity.In this paper,inspired by the human spine,we propose a novel bionic human spine inspired quasi-zero stiffness(QZS)vibration isolator which consists of a cascaded multi-stage negative stiffness structure.The force and stiffness characteristics are investigated first,the dynamic model is established by Newton’s second law,and the isolation performance is analyzed by the harmonic balance method(HBM).Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages,and reducing the damping values and external force values can obtain better low-frequency isolation performance.In comparison with the linear structure and existing traditional QZS isolator,the bionic spine isolator has better vibration isolation performance in low-frequency regions.It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications.展开更多
Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key c...Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key components.The support system,an important part of TBM,is one path through which vibrational energy from the cutter head is transmitted.To reduce the vibration of support systems of TBM during the excavation process,based on the structural features of the support hydraulic system,a nonlinear dynamical model of support hydraulic systems of TBM is established.The influences of the component structure parameters and operating conditions parameters on the stiffness characteristics of the support hydraulic system are analyzed.The analysis results indicate that the static stiffness of the support hydraulic system consists of an increase stage,stable stage and decrease stage.The static stiffness value increases with an increase in the clearances.The pre-compression length of the spring in the relief valve a ects the range of the stable stage of the static stiffness,and it does not a ect the static stiffness value.The dynamic stiffness of the support hydraulic system consists of a U-shape and reverse U-shape.The bottom value of the U-shape increases with the amplitude and frequency of the external force acting on the cylinder body,however,the top value of the reverse U-shape remains constant.This study instructs how to design the support hydraulic system of TBM.展开更多
Existing quasi-zero stiffness(QZS)isolators are reviewed.In terms of their advantages,a novel X-shape QZS isolator combined with the cam-roller-spring mechanism(CRSM)is proposed.Different from the existing X-shape iso...Existing quasi-zero stiffness(QZS)isolators are reviewed.In terms of their advantages,a novel X-shape QZS isolator combined with the cam-roller-spring mechanism(CRSM)is proposed.Different from the existing X-shape isolators,oblique springs are used to enhance the negative stiffness of the system.Meanwhile,the CRSM is used to eliminate the gravity of the loading mass,while the X-shape structure leaves its static position.The existing QZS isolators are demonstrated and classified according to their nonlinearity mechanisms and classical shapes.It is shown that the oblique spring can realize negative stiffness based on the simplest mechanism.The X-shape has a strong capacity of loading mass,while the CRSM can achieve a designed restoring force at any position.The proposed isolator combines all these advantages together.Based on the harmonic balance method(HBM)and the simulation,the displacement transmissibilities of the proposed isolator,the X-shape isolators just with oblique springs,and the X-shape isolators in the traditional form are studied.The results show that the proposed isolator has the lowest beginning isolation frequency and the smallest maximum displacement transmissibility.However,it still has some disadvantages similar to the existing QZS isolators.This means that its parameters should be designed carefully so as to avoid becoming a bistable system,in which there are two potential wells in the potential energy curve and thus the isolation performance will be worsened.展开更多
Wave energy is one of the most abundant renewable clean energy sources,and has been widely studied because of its advantages of continuity and low seasonal variation.However,its low capture efficiency and narrow captu...Wave energy is one of the most abundant renewable clean energy sources,and has been widely studied because of its advantages of continuity and low seasonal variation.However,its low capture efficiency and narrow capture frequency bandwidth are still technical bottlenecks that restrict the commercial application of wave energy converters(WECs).In recent years,using a nonlinear stiffness mechanism(NSM)for passive control has provided a new way to solve these technical bottlenecks.This literature review focuses on the research performed on the use of nonlinear mechanisms in wave energy device utilization,including the conceptual design of a mechanism,hydrodynamic models,dynamic characteristics,response mechanisms,and some examples of experimental verification.Finally,future research directions are discussed and recommended.展开更多
Being different from avoidance of singularity of closed-loop linkages, this paper employs the kinematic singularity to construct compliant mechanisms with expected nonlinear stiffness characteristics to enrich the met...Being different from avoidance of singularity of closed-loop linkages, this paper employs the kinematic singularity to construct compliant mechanisms with expected nonlinear stiffness characteristics to enrich the methods of compliant mechanisms synthesis. The theory for generating kinetostatic nonlinear stiffness characteristic by the kinematic limb-singularity of a crank-slider linkage is developed. Based on the principle of virtual work, the kinetostatic model of the crank-linkage with springs is established. The influences of spring stiffness on the toque-position angle relation are analyzed. It indicates that corresponding spring stiffness may generate one of four types of nonlinear stiffness characteristics including the bi-stable, local negative-stiffness, zero-stiffness or positive-stiffness when the mechanism works around the kinematic limb-singularity position. Thus the compliant mechanism with an expected stiffness characteristic can be constructed by employing the pseudo rigid-body model of the mechanism whose joints or links are replaced by corresponding flexures. Finally, a tri-symmetrical constant-torque compliant mechanism is fabricated, where the curve of torque-position angle is obtained by an experimental testing. The measurement indicates that the compliant mechanism can generate a nearly constant-torque zone.展开更多
The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches....The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.展开更多
Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design ...Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.展开更多
Vibration absorption efficiency of a variable⁃stiffness nonlinear energy sink(NES)was investigated when the main oscillator was subjected to harmonic and impulse excitations.The slow flow equations of the coupled syst...Vibration absorption efficiency of a variable⁃stiffness nonlinear energy sink(NES)was investigated when the main oscillator was subjected to harmonic and impulse excitations.The slow flow equations of the coupled system were derived by using the complexification⁃averaging method,and the nonlinear equations which describe the steady⁃state response were obtained.As the harmonic excitation force increased,the system which comprises constant⁃stiffness NES generated higher branch responses,greatly reducing the vibration absorption efficiency.The influence of nonlinear stiffness on the responses of the system was investigated.Results show that,with the increase of harmonic exciting force,a reduction of NES stiffness can eliminate the higher branch responses and even the frequency band of strongly modulated responses.The vibration absorption efficiency of variable⁃stiffness NES attached to the linear oscillator for different amplitudes of impulse excitation was investigated.Results show that the proper reduction of nonlinear stiffness under increasing impulse excitation can greatly increase the vibration absorption efficiency of NES,and the variable⁃stiffness design can effectively mitigate the negative influences of the increase of the excitation amplitude on the efficiency of constant⁃stiffness NES.展开更多
Combining disk springs having negative stiffness with a rolling-ball in parallel is proposed in this paper. It is used to reduce the system stiffness and the positioning error in a non-ideal environment.The characteri...Combining disk springs having negative stiffness with a rolling-ball in parallel is proposed in this paper. It is used to reduce the system stiffness and the positioning error in a non-ideal environment.The characteristics of a disk spring are analyzed. The dynamic equation of its motion has been obtained based on Newton's second law. After definition of a error margin,the dynamic equation of the motion can be treated as a Duffing oscillator,and the influences of non-dimensional parameters on the stiffness and transmissibility are studied. The natural frequency and transmissibility are achieved in a linearization range,where the ratio of linear to nonlinear items is small enough.The influence of mass ratio and non-dimensional parameters on natural frequency are analyzed. Finally,a comparison of numerical example demonstrates that the QZS system can realize a lower stiffness within an increased range.展开更多
In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results ...In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results given in our paper will be of great importance to the analyses of nonlinear numerical and nonlinear stability in finite element methods.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
To achieve stability optimization in low-frequency vibration control for precision instruments,this paper presents a quasi-zero stiffness(QZS)vibration isolator with adjustable nonlinear stiffness.Additionally,the str...To achieve stability optimization in low-frequency vibration control for precision instruments,this paper presents a quasi-zero stiffness(QZS)vibration isolator with adjustable nonlinear stiffness.Additionally,the stress-magnetism coupling model is established through meticulous theoretical derivation.The controllable QZS interval is constructed via parameter design and magnetic control,effectively segregating the high static stiffness bearing section from the QZS vibration isolation section.Furthermore,a displacement control scheme utilizing a magnetic force is proposed to regulate entry into the QZS working range for the vibration isolation platform.Experimental results demonstrate that the operation within this QZS region reduces the peak-to-peak acceleration signal by approximately 66.7%compared with the operation outside this region,thereby significantly improving the low frequency performance of the QZS vibration isolator.展开更多
In this paper,triple quasi-zero stiffness(QZS)passive vibration isolators whose restoring force curve has a three-stage softening effect are proposed.Multi-coupled SD oscillators with three independent geometrical par...In this paper,triple quasi-zero stiffness(QZS)passive vibration isolators whose restoring force curve has a three-stage softening effect are proposed.Multi-coupled SD oscillators with three independent geometrical parameters are used as negative stiffness mechanisms to achieve QZS characteristics at the origin and symmetrical positions on both sides of the origin.Isolation performances of different triple QZS isolators are analyzed to show influences of the selection of QZS regions away from the origin on the range of isolation regions.Pareto optimizations of system parameters are carried out to get a larger range of small restoring force regions and small stiffness regions.Isolation performances of two triple QZS isolators are discussed to show the influence of different Pareto optimization solutions through the comparisons with single and double QZS isolators.Results showed that triple QZS isolators have both the advantages of single and double QZS isolators which results in better isolation performances under both small and large excitation amplitudes.An improvement in isolation performances for triple QZS isolators is found with the decrease in average stiffness due to the appearance of two symmetrical QZS regions away from the origin.Larger displacements of QZS regions away from the origin result in better isolation performances when excitation amplitude is large,and triple QZS characteristics are similar to double QZS isolators at this time.Smaller restoring forces of QZS regions away from the origin lead to better isolation performances when excitation amplitude is small,and triple QZS characteristics are similar to single QZS isolators at this moment.Compared with the decrease in average stiffness,the improvement of isolation performances shows a hysteresis phenomenon due to the difference between static and dynamic characteristics.展开更多
Passive vibration isolation systems have been widely applied due to their low power consumption and high reliability.Nevertheless,the design of vibration isolators is usually limited by the narrow space of installatio...Passive vibration isolation systems have been widely applied due to their low power consumption and high reliability.Nevertheless,the design of vibration isolators is usually limited by the narrow space of installation,and the requirement of heavy loads needs the high supporting stiffness that leads to the narrow isolation frequency band.To improve the vibration isolation performance of passive isolation systems for dynamic loaded equipment,a novel modular quasi-zero stiffness vibration isolator(MQZS-VI)with high linearity and integrated fluid damping is proposed.The MQZS-VI can achieve high-performance vibration isolation under a constraint mounted space,which is realized by highly integrating a novel combined magnetic negative stiffness mechanism into a damping structure:The stator magnets are integrated into the cylinder block,and the moving magnets providing negative-stiffness force also function as the piston supplying damping force simultaneously.An analytical model of the novel MQZS-VI is established and verified first.The effects of geometric parameters on the characteristics of negative stiffness and damping are then elucidated in detail based on the analytical model,and the design procedure is proposed to provide guidelines for the performance optimization of the MQZS-VI.Finally,static and dynamic experiments are conducted on the prototype.The experimental results demonstrate the proposed analytical model can be effectively utilized in the optimal design of the MQZS-VI,and the optimized MQZS-VI broadened greatly the isolation frequency band and suppressed the resonance peak simultaneously,which presented a substantial potential for application in vibration isolation for dynamic loaded equipment.展开更多
The existing constitutive models of rock with strain softening cannot successfully reflect the damageinduced anisotropy and nonlinearity of the post-peak failure behavior under progressive loading. In order to better ...The existing constitutive models of rock with strain softening cannot successfully reflect the damageinduced anisotropy and nonlinearity of the post-peak failure behavior under progressive loading. In order to better reflect the nonlinear stress-strain behavior of rock, especially for the post-peak failure behavior,with expected stiffness degradation and large deformation, a modified constitutive model of rock considering stiffness degradation and dilatation behavior at large deformation was proposed in this study. This study analyzes and discusses various attenuation parameters in the proposed nonlinear plastic constitutive model using FLAC^(3D) software. The excavation-induced stress in rocks was calculated by FLAC^(3D) using the Mohr-Coulomb model, conventional strain model, and the proposed modified model. The obtained results of these models were analyzed and compared with field data. This study shows that the simulated results using the proposed new constitutive model matched much more closely with the measured field data, with an average error less than 5%. This new model can successfully reflect the damage-induced stiffness degradation at large deformation, and can provide a theoretical basis for stability design and evaluation of underground excavation.展开更多
Most references on hydropneumatic suspension analysis regard it as harden Duffing spring and take the white noise as the system input, which is quite different from real physical model. It will introduce considerable ...Most references on hydropneumatic suspension analysis regard it as harden Duffing spring and take the white noise as the system input, which is quite different from real physical model. It will introduce considerable errors to the analytical result compared with the numerical simulation which makes it impossible to give a good depiction of the hydropneumatic suspension dynamics. In this paper, the dynamic response of the hydropneumatic suspension is worked out using statistical linearization based on 2 DOFs nonlinear suspension model. The damping of the suspension and the tire stiffness are both regarded as linear components and the real road roughness spectrum is used to work out the system input. The explicit analytical equivalent stiffness, dynamic mean value offset from statistic equilibrium position and the sprung acceleration varied with parameters of hydropneumatic spring, road roughness and vehicle velocity are worked out by substituting the nonlinear stiffness of hydropneumatic spring with its first three terms Tyler series at the static equilibrium position using James formula. The comparison of the numerical simulation and analytical result both on statistical parameters and distribution shows the validity of the analysis. The explicit form provides a concise and valid method on hydropneumatic suspension design and optimization.展开更多
The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly ...The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly analyzed from the viewpoint of equivalent damping. Firstly, the primary resonance of the controlled HSLDS vibration isolator subjected to a harmonic force excitation is obtained based on the multiple scales method and further verified by numerical integration. The stability of the primary resonance is subsequently investigated. Then, the equivalent damping is defined to study the effects of feedback gain and time delay on primary resonance. The condition of jump avoidance is obtained with the purpose of eliminating the adverse effects induced by jumps. Finally, the force transmissibility of the controlled HSLDS vibration isolator is defined to evaluate its isolation performance. It is shown that an appropriate choice of feedback parameters can effectively suppress the force transmissibility in resonant region and reduce the resonance frequency. Furthermore, a wider vibration isolation frequency bandwidth can be achieved compared to the passive HSLDS vibration isolator.展开更多
In this paper, a semiactive variable stiffness (SVS) device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS d...In this paper, a semiactive variable stiffness (SVS) device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS device is presented. The ON/OFF control algorithm is used to operate the SVS control device. The vibration response of the cable with the SVS device is numerically studied for a variety of additional stiffness combinations in both the frequency and time domains and for both parametric and classical resonance vibration conditions. The numerical studies further consider the cable sag effect. From the numerical results, it is shown that the SVS device effectively suppresses the cable resonance vibration response, and as the stiffness of the device increases, the device achieves greater suppression of vibration. Moreover, it was shown that the SVS device increases the critical axial displacement of the excitation under cable parametric vibration conditions.展开更多
In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties...In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.展开更多
An easily stackable multi-layer quasi-zero-stiffness(ML-QZS)meta-structure is proposed to achieve highly efficient vibration isolation performance at low frequency.First,the distributed shape optimization method is us...An easily stackable multi-layer quasi-zero-stiffness(ML-QZS)meta-structure is proposed to achieve highly efficient vibration isolation performance at low frequency.First,the distributed shape optimization method is used to design the unit cel,i.e.,the single-layer QZS(SL-QZS)meta-structure.Second,the stiffness feature of the unit cell is investigated and verified through static experiments.Third,the unit cells are stacked one by one along the direction of vibration isolation,and thus the ML-QZS meta-structure is constructed.Fourth,the dynamic modeling of the ML-QZS vibration isolation metastructure is conducted,and the dynamic responses are obtained from the equations of motion,and verified by finite element(FE)simulations.Finally,a prototype of the ML-QZS vibration isolation meta-structure is fabricated by additive manufacturing,and the vibration isolation performance is evaluated experimentally.The results show that the vibration isolation performance substantially enhances when the number of unit cells increases.More importantly,the ML-QZS meta-structure can be easily extended in the direction of vibration isolation when the unit cells are properly stacked.Hence,the ML-FQZS vibration isolation meta-structure should be a fascinating solution for highly efficient vibration isolation performance at low frequency.展开更多
基金supported by the National Natural Science Foundation of China(No.12072221)the Natural Science Foundation of Liaoning Province of China(No.2019-KF-01-09)。
文摘Human motion induced vibration has very low frequency,ranging from 2 Hz to 5 Hz.Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity.In this paper,inspired by the human spine,we propose a novel bionic human spine inspired quasi-zero stiffness(QZS)vibration isolator which consists of a cascaded multi-stage negative stiffness structure.The force and stiffness characteristics are investigated first,the dynamic model is established by Newton’s second law,and the isolation performance is analyzed by the harmonic balance method(HBM).Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages,and reducing the damping values and external force values can obtain better low-frequency isolation performance.In comparison with the linear structure and existing traditional QZS isolator,the bionic spine isolator has better vibration isolation performance in low-frequency regions.It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications.
基金Supported by National Key R&D Program of China(Grant No.2018YFB1702503)National Program on Key Basic Research Project of China(973 Program,Grant No.2013CB035403)Startup Fund for Youngman Research at SJTU(SFYR at SJTU)
文摘Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key components.The support system,an important part of TBM,is one path through which vibrational energy from the cutter head is transmitted.To reduce the vibration of support systems of TBM during the excavation process,based on the structural features of the support hydraulic system,a nonlinear dynamical model of support hydraulic systems of TBM is established.The influences of the component structure parameters and operating conditions parameters on the stiffness characteristics of the support hydraulic system are analyzed.The analysis results indicate that the static stiffness of the support hydraulic system consists of an increase stage,stable stage and decrease stage.The static stiffness value increases with an increase in the clearances.The pre-compression length of the spring in the relief valve a ects the range of the stable stage of the static stiffness,and it does not a ect the static stiffness value.The dynamic stiffness of the support hydraulic system consists of a U-shape and reverse U-shape.The bottom value of the U-shape increases with the amplitude and frequency of the external force acting on the cylinder body,however,the top value of the reverse U-shape remains constant.This study instructs how to design the support hydraulic system of TBM.
基金the National Natural Science Foundation of China(No.12002195)the National Science Fund for Distinguished Young Scholars of China(No.12025204)+1 种基金the Program of Shanghai Municipal Education Commission of China(No.2019-01-07-00-09-E00018)the Pujiang Project of Shanghai Science and Technology Commission of China(No.20PJ1404000)。
文摘Existing quasi-zero stiffness(QZS)isolators are reviewed.In terms of their advantages,a novel X-shape QZS isolator combined with the cam-roller-spring mechanism(CRSM)is proposed.Different from the existing X-shape isolators,oblique springs are used to enhance the negative stiffness of the system.Meanwhile,the CRSM is used to eliminate the gravity of the loading mass,while the X-shape structure leaves its static position.The existing QZS isolators are demonstrated and classified according to their nonlinearity mechanisms and classical shapes.It is shown that the oblique spring can realize negative stiffness based on the simplest mechanism.The X-shape has a strong capacity of loading mass,while the CRSM can achieve a designed restoring force at any position.The proposed isolator combines all these advantages together.Based on the harmonic balance method(HBM)and the simulation,the displacement transmissibilities of the proposed isolator,the X-shape isolators just with oblique springs,and the X-shape isolators in the traditional form are studied.The results show that the proposed isolator has the lowest beginning isolation frequency and the smallest maximum displacement transmissibility.However,it still has some disadvantages similar to the existing QZS isolators.This means that its parameters should be designed carefully so as to avoid becoming a bistable system,in which there are two potential wells in the potential energy curve and thus the isolation performance will be worsened.
基金the State Key Laboratory of Coastal and Offshore Engineering of China(No.LP2019)the 2020 Research Program of Sanya Yazhou Bay Science and Technology City of China(No.SKJC-2020-01-006)+1 种基金the Hainan Provincial Natural Science Foundation of China(No.520QN290)the High-tech Ship Research Projects Sponsored by MIIT of China(No.[2019]357)。
文摘Wave energy is one of the most abundant renewable clean energy sources,and has been widely studied because of its advantages of continuity and low seasonal variation.However,its low capture efficiency and narrow capture frequency bandwidth are still technical bottlenecks that restrict the commercial application of wave energy converters(WECs).In recent years,using a nonlinear stiffness mechanism(NSM)for passive control has provided a new way to solve these technical bottlenecks.This literature review focuses on the research performed on the use of nonlinear mechanisms in wave energy device utilization,including the conceptual design of a mechanism,hydrodynamic models,dynamic characteristics,response mechanisms,and some examples of experimental verification.Finally,future research directions are discussed and recommended.
基金Supported by National Natural Science Foundation of China(Grant No.51605006)Research Foundation of Key Laboratory of Manufacturing Systems and Advanced Technology of Guangxi Province,China(Grant No.17-259-05-013K)
文摘Being different from avoidance of singularity of closed-loop linkages, this paper employs the kinematic singularity to construct compliant mechanisms with expected nonlinear stiffness characteristics to enrich the methods of compliant mechanisms synthesis. The theory for generating kinetostatic nonlinear stiffness characteristic by the kinematic limb-singularity of a crank-slider linkage is developed. Based on the principle of virtual work, the kinetostatic model of the crank-linkage with springs is established. The influences of spring stiffness on the toque-position angle relation are analyzed. It indicates that corresponding spring stiffness may generate one of four types of nonlinear stiffness characteristics including the bi-stable, local negative-stiffness, zero-stiffness or positive-stiffness when the mechanism works around the kinematic limb-singularity position. Thus the compliant mechanism with an expected stiffness characteristic can be constructed by employing the pseudo rigid-body model of the mechanism whose joints or links are replaced by corresponding flexures. Finally, a tri-symmetrical constant-torque compliant mechanism is fabricated, where the curve of torque-position angle is obtained by an experimental testing. The measurement indicates that the compliant mechanism can generate a nearly constant-torque zone.
基金Project supported by the National Natural Science Foundation of China(Nos.11832002 and 12072201)。
文摘The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.
基金the China National Funds for Distinguished Young Scholars(No.12025204)。
文摘Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.
基金Sponsored by the National Natural Science Foundation of China(Grant Nos.11402170 and 11402165)the Tianjin Natural Science Foundation of China(Grant Nos.17JCYBJC18800 and 17JCZDJC38500)
文摘Vibration absorption efficiency of a variable⁃stiffness nonlinear energy sink(NES)was investigated when the main oscillator was subjected to harmonic and impulse excitations.The slow flow equations of the coupled system were derived by using the complexification⁃averaging method,and the nonlinear equations which describe the steady⁃state response were obtained.As the harmonic excitation force increased,the system which comprises constant⁃stiffness NES generated higher branch responses,greatly reducing the vibration absorption efficiency.The influence of nonlinear stiffness on the responses of the system was investigated.Results show that,with the increase of harmonic exciting force,a reduction of NES stiffness can eliminate the higher branch responses and even the frequency band of strongly modulated responses.The vibration absorption efficiency of variable⁃stiffness NES attached to the linear oscillator for different amplitudes of impulse excitation was investigated.Results show that the proper reduction of nonlinear stiffness under increasing impulse excitation can greatly increase the vibration absorption efficiency of NES,and the variable⁃stiffness design can effectively mitigate the negative influences of the increase of the excitation amplitude on the efficiency of constant⁃stiffness NES.
基金Supported by National Science and Technology Major Project(2013ZX02104003)
文摘Combining disk springs having negative stiffness with a rolling-ball in parallel is proposed in this paper. It is used to reduce the system stiffness and the positioning error in a non-ideal environment.The characteristics of a disk spring are analyzed. The dynamic equation of its motion has been obtained based on Newton's second law. After definition of a error margin,the dynamic equation of the motion can be treated as a Duffing oscillator,and the influences of non-dimensional parameters on the stiffness and transmissibility are studied. The natural frequency and transmissibility are achieved in a linearization range,where the ratio of linear to nonlinear items is small enough.The influence of mass ratio and non-dimensional parameters on natural frequency are analyzed. Finally,a comparison of numerical example demonstrates that the QZS system can realize a lower stiffness within an increased range.
文摘In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results given in our paper will be of great importance to the analyses of nonlinear numerical and nonlinear stability in finite element methods.
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Project supported by the National Natural Science Foundation of China(Nos.12372187,52321003,12302250)the Fundamental Research Funds for the Central Universities(Nos.KY2090000094 and WK2480000010)+2 种基金the Fellowship of China Postdoctoral Science Foundation(Nos.2024M753103 and 2023M733388)the University Synergy Innovation Program of Anhui Province(No.GXXT-2023-024)the CAS Talent Introduction Program(No.KJ2090007006)。
文摘To achieve stability optimization in low-frequency vibration control for precision instruments,this paper presents a quasi-zero stiffness(QZS)vibration isolator with adjustable nonlinear stiffness.Additionally,the stress-magnetism coupling model is established through meticulous theoretical derivation.The controllable QZS interval is constructed via parameter design and magnetic control,effectively segregating the high static stiffness bearing section from the QZS vibration isolation section.Furthermore,a displacement control scheme utilizing a magnetic force is proposed to regulate entry into the QZS working range for the vibration isolation platform.Experimental results demonstrate that the operation within this QZS region reduces the peak-to-peak acceleration signal by approximately 66.7%compared with the operation outside this region,thereby significantly improving the low frequency performance of the QZS vibration isolator.
基金supported by the National Natural Science Foundation of China(Grant No.11732006)。
文摘In this paper,triple quasi-zero stiffness(QZS)passive vibration isolators whose restoring force curve has a three-stage softening effect are proposed.Multi-coupled SD oscillators with three independent geometrical parameters are used as negative stiffness mechanisms to achieve QZS characteristics at the origin and symmetrical positions on both sides of the origin.Isolation performances of different triple QZS isolators are analyzed to show influences of the selection of QZS regions away from the origin on the range of isolation regions.Pareto optimizations of system parameters are carried out to get a larger range of small restoring force regions and small stiffness regions.Isolation performances of two triple QZS isolators are discussed to show the influence of different Pareto optimization solutions through the comparisons with single and double QZS isolators.Results showed that triple QZS isolators have both the advantages of single and double QZS isolators which results in better isolation performances under both small and large excitation amplitudes.An improvement in isolation performances for triple QZS isolators is found with the decrease in average stiffness due to the appearance of two symmetrical QZS regions away from the origin.Larger displacements of QZS regions away from the origin result in better isolation performances when excitation amplitude is large,and triple QZS characteristics are similar to double QZS isolators at this time.Smaller restoring forces of QZS regions away from the origin lead to better isolation performances when excitation amplitude is small,and triple QZS characteristics are similar to single QZS isolators at this moment.Compared with the decrease in average stiffness,the improvement of isolation performances shows a hysteresis phenomenon due to the difference between static and dynamic characteristics.
基金supported by the National Key R&D Program of China(Grant Nos.2020YFB2007300 and 2020YFB2007601)the National Natural Science Foundation of China(Grant Nos.52075193,52305107,and 52275112)+1 种基金the National Science and Technology Major Project of China(Grant No.2017ZX02101007-002)the Postdoctoral Science Foundation of China(Grant No.2022M711250).
文摘Passive vibration isolation systems have been widely applied due to their low power consumption and high reliability.Nevertheless,the design of vibration isolators is usually limited by the narrow space of installation,and the requirement of heavy loads needs the high supporting stiffness that leads to the narrow isolation frequency band.To improve the vibration isolation performance of passive isolation systems for dynamic loaded equipment,a novel modular quasi-zero stiffness vibration isolator(MQZS-VI)with high linearity and integrated fluid damping is proposed.The MQZS-VI can achieve high-performance vibration isolation under a constraint mounted space,which is realized by highly integrating a novel combined magnetic negative stiffness mechanism into a damping structure:The stator magnets are integrated into the cylinder block,and the moving magnets providing negative-stiffness force also function as the piston supplying damping force simultaneously.An analytical model of the novel MQZS-VI is established and verified first.The effects of geometric parameters on the characteristics of negative stiffness and damping are then elucidated in detail based on the analytical model,and the design procedure is proposed to provide guidelines for the performance optimization of the MQZS-VI.Finally,static and dynamic experiments are conducted on the prototype.The experimental results demonstrate the proposed analytical model can be effectively utilized in the optimal design of the MQZS-VI,and the optimized MQZS-VI broadened greatly the isolation frequency band and suppressed the resonance peak simultaneously,which presented a substantial potential for application in vibration isolation for dynamic loaded equipment.
文摘The existing constitutive models of rock with strain softening cannot successfully reflect the damageinduced anisotropy and nonlinearity of the post-peak failure behavior under progressive loading. In order to better reflect the nonlinear stress-strain behavior of rock, especially for the post-peak failure behavior,with expected stiffness degradation and large deformation, a modified constitutive model of rock considering stiffness degradation and dilatation behavior at large deformation was proposed in this study. This study analyzes and discusses various attenuation parameters in the proposed nonlinear plastic constitutive model using FLAC^(3D) software. The excavation-induced stress in rocks was calculated by FLAC^(3D) using the Mohr-Coulomb model, conventional strain model, and the proposed modified model. The obtained results of these models were analyzed and compared with field data. This study shows that the simulated results using the proposed new constitutive model matched much more closely with the measured field data, with an average error less than 5%. This new model can successfully reflect the damage-induced stiffness degradation at large deformation, and can provide a theoretical basis for stability design and evaluation of underground excavation.
基金Supported by National Natural Science Foundation of China(Grant No.51005018)Beijing Municipal Clean Vehicle Key Laboratory Open Foundation of China(2013)
文摘Most references on hydropneumatic suspension analysis regard it as harden Duffing spring and take the white noise as the system input, which is quite different from real physical model. It will introduce considerable errors to the analytical result compared with the numerical simulation which makes it impossible to give a good depiction of the hydropneumatic suspension dynamics. In this paper, the dynamic response of the hydropneumatic suspension is worked out using statistical linearization based on 2 DOFs nonlinear suspension model. The damping of the suspension and the tire stiffness are both regarded as linear components and the real road roughness spectrum is used to work out the system input. The explicit analytical equivalent stiffness, dynamic mean value offset from statistic equilibrium position and the sprung acceleration varied with parameters of hydropneumatic spring, road roughness and vehicle velocity are worked out by substituting the nonlinear stiffness of hydropneumatic spring with its first three terms Tyler series at the static equilibrium position using James formula. The comparison of the numerical simulation and analytical result both on statistical parameters and distribution shows the validity of the analysis. The explicit form provides a concise and valid method on hydropneumatic suspension design and optimization.
基金Project(KYLX15_0256)supported by the Funding of Jiangsu Innovation Program for Graduate Education,ChinaProject(SV2015-KF-01)supported by the Open Project of State Key Laboratory for Strength and Vibration of Mechanical Structures,ChinaProject(XZA15003)supported by the Fundamental Research Funds for the Central Universities,China
文摘The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly analyzed from the viewpoint of equivalent damping. Firstly, the primary resonance of the controlled HSLDS vibration isolator subjected to a harmonic force excitation is obtained based on the multiple scales method and further verified by numerical integration. The stability of the primary resonance is subsequently investigated. Then, the equivalent damping is defined to study the effects of feedback gain and time delay on primary resonance. The condition of jump avoidance is obtained with the purpose of eliminating the adverse effects induced by jumps. Finally, the force transmissibility of the controlled HSLDS vibration isolator is defined to evaluate its isolation performance. It is shown that an appropriate choice of feedback parameters can effectively suppress the force transmissibility in resonant region and reduce the resonance frequency. Furthermore, a wider vibration isolation frequency bandwidth can be achieved compared to the passive HSLDS vibration isolator.
基金National Natural Science Foundation of China Under Grant No. 50178025
文摘In this paper, a semiactive variable stiffness (SVS) device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS device is presented. The ON/OFF control algorithm is used to operate the SVS control device. The vibration response of the cable with the SVS device is numerically studied for a variety of additional stiffness combinations in both the frequency and time domains and for both parametric and classical resonance vibration conditions. The numerical studies further consider the cable sag effect. From the numerical results, it is shown that the SVS device effectively suppresses the cable resonance vibration response, and as the stiffness of the device increases, the device achieves greater suppression of vibration. Moreover, it was shown that the SVS device increases the critical axial displacement of the excitation under cable parametric vibration conditions.
文摘In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.
基金supported by the National Natural Science Foundation of China(Nos.12122206 and 12272129)the Natural Science Foundation of Hunan Province of China(No.2024JJ4004)the Zhejiang Provincial Natural Science Foundation of China(No.LQ24A020006)。
文摘An easily stackable multi-layer quasi-zero-stiffness(ML-QZS)meta-structure is proposed to achieve highly efficient vibration isolation performance at low frequency.First,the distributed shape optimization method is used to design the unit cel,i.e.,the single-layer QZS(SL-QZS)meta-structure.Second,the stiffness feature of the unit cell is investigated and verified through static experiments.Third,the unit cells are stacked one by one along the direction of vibration isolation,and thus the ML-QZS meta-structure is constructed.Fourth,the dynamic modeling of the ML-QZS vibration isolation metastructure is conducted,and the dynamic responses are obtained from the equations of motion,and verified by finite element(FE)simulations.Finally,a prototype of the ML-QZS vibration isolation meta-structure is fabricated by additive manufacturing,and the vibration isolation performance is evaluated experimentally.The results show that the vibration isolation performance substantially enhances when the number of unit cells increases.More importantly,the ML-QZS meta-structure can be easily extended in the direction of vibration isolation when the unit cells are properly stacked.Hence,the ML-FQZS vibration isolation meta-structure should be a fascinating solution for highly efficient vibration isolation performance at low frequency.