Quasi-zero-stiffness(QZS)metamaterials have attracted significant interest for application in low-frequency vibration isolation.However,previous work has been limited by the design mechanism of QZS metamaterials,as it...Quasi-zero-stiffness(QZS)metamaterials have attracted significant interest for application in low-frequency vibration isolation.However,previous work has been limited by the design mechanism of QZS metamaterials,as it is still difficult to achieve a simplified structure suitable for practical engineering applications.Here,we introduce a class of programmable QZS metamaterials and a novel design mechanism that address this long-standing difficulty.The proposed QZS metamaterials are formed by an array of representative unit cells(RUCs)with the expected QZS features,where the QZS features of the RUC are tailored by means of a structural bionic mechanism.In our experiments,we validate the QZS features exhibited by the RUCs,the programmable QZS behavior,and the potential promising applications of these programmable QZS metamaterials in low-frequency vibration isolation.The obtained results could inspire a new class of programmable QZS metamaterials for low-frequency vibration isolation in current and future mechanical and other engineering applications.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
Traditional linear vibration isolators struggle to combine high load-bearing capacity with low-frequency vibration isolation, whereas nonlinear metastructure isolators can effectively fulfill both functions. This pape...Traditional linear vibration isolators struggle to combine high load-bearing capacity with low-frequency vibration isolation, whereas nonlinear metastructure isolators can effectively fulfill both functions. This paper draws inspiration from the Quasi-Zero Stiffness (QZS) characteristics resulting from the buckling deformation of beams, and proposes a gear-based QZS structure by arranging beams in a circular array. We investigated the static mechanical behavior under different structural parameters, loading angles, and gear combinations through experiments and simulations, and demonstrated the mechanical performances could be effectively programmed. Subsequent vibration isolation tests on the double gears prove superior vibration isolation performance at low frequency while maintaining high load-bearing capacities. Additionally, a key contribution of our work is the development of a mathematical model to characterize the buckling behavior of the unit beam within the gear structure, with its accuracy validated through finite element analysis and experimental results. The gear’s modulus, number of teeth, and pressure angle are selected according to standard series, allowing the gear can be seamlessly integrated into existing mechanical systems in critical fields such as aerospace, military, and etc.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
Bionic X-shaped vibration isolators have been widely employed in aerospace and other industrial fields,but the stiffness properties of classic X-shaped structures limit the vibration isolation ability for low frequenc...Bionic X-shaped vibration isolators have been widely employed in aerospace and other industrial fields,but the stiffness properties of classic X-shaped structures limit the vibration isolation ability for low frequencies.An innovative bionic quasi-zero stiffness(QZS)vibration isolator(BQZSVI),which can broaden the QZS range of a classic X-shaped isolator and can bring it closer to the equilibrium position,is proposed.The BQZSVI consists of an X-shaped structure as the bone fabric of lower limbs and a nonlinear magnetic loop device simulating the leg muscle.Based on static calculation,the stiffness characteristic of the structure is confirmed.The governing equations of motion of the BQZSVI structure are established in the framework of the Lagrange equation,and the harmonic balance method(HBM)is adopted to obtain the transmissibility responses.The results show that the BQZSVI can provide a more accessible and broader range of QZS.In the dynamic manifestation,the introduction of the BQZSVI can reduce the amplitude of a classic X-shaped vibration isolator by 65.7%,and bring down the initial vibration isolation frequency from 7.43 Hz to 2.39 Hz.In addition,a BQZSVI prototype is designed and fabricated,and the exactitude of the theoretical analysis method is proven by means of experiments.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
Vibration reduction has always been one of hot and important topics in mechanical engineering,especially for the special measurement instrument.In this paper,a novel limb-inspired bionic structure is proposed to gener...Vibration reduction has always been one of hot and important topics in mechanical engineering,especially for the special measurement instrument.In this paper,a novel limb-inspired bionic structure is proposed to generate negative stiffness and design a new quasi-zero stiffness isolator via torsion springs,distinguishing from the existing tension spring structures in the literature.The nonlinear mathematical model of the proposed structure is developed and the corresponding dynamic properties are further investigated by using the Harmonic Balance method and ADAMS verification.To evaluate the vibration isolation performance,typical three-springs quasi-zero stiffness(TS QZS)system is selected to compare with the proposed bionic structure.And the graphical processing unit(GPU)parallel technology is applied to perform necessary two-parameter analyses,providing more insights into the effects of parameters on the transmissibility.It is shown that the proposed structure can show advantages over the typical TS QZS system in a wider vibration isolation range for harmonic excitation case and shorter decay time for the impact excitation case.展开更多
To improve the vibration isolation performance of suspensions,various new structural forms of suspensions have been proposed.However,there is uncertainty in these new structure suspensions,so the deterministic researc...To improve the vibration isolation performance of suspensions,various new structural forms of suspensions have been proposed.However,there is uncertainty in these new structure suspensions,so the deterministic research cannot refect the performance of the suspension under actual operating conditions.In this paper,a quasi-zero stifness isolator is used in automotive suspensions to form a new suspension−quasi-zero stifness air suspension(QZSAS).Due to the strong nonlinearity and structural complexity of quasi-zero stifness suspensions,changes in structural parameters may cause dramatic changes in suspension performance,so it is of practical importance to study the efect of structural parameter uncertainty on the suspension performance.In order to solve this problem,three suspension structural parameters d_(0),L_(0) and Pc_(0) are selected as random variables,and the polynomial chaos expansion(PCE)theory is used to solve the suspension performance parameters.The sensitivity of the performance parameters to diferent structural parameters was discussed and analyzed in the frequency domain.Furthermore,a multi-objective optimization of the structural parameters d_(0),L_(0) and Pc_(0) of QZSAS was performed with the mean and variance of the root-mean-square(RMS)acceleration values as the optimization objectives.The optimization results show that there is an improvement of about 8%−1_(0)%in the mean value and about 4_(0)%−55%in the standard deviation of acceleration(RMS)values.This paper verifes the feasibility of the PCE method for solving the uncertainty problem of complex nonlinear systems,which provide a reference for the future structural design and optimization of such suspension systems.展开更多
The stratospheric quasi-zero wind layer (QZWL) is a transition region with low zonal wind speeds in the lower stratosphere at an altitude of ~20 km. The zonal wind direction above the QZWL layer is opposite to that be...The stratospheric quasi-zero wind layer (QZWL) is a transition region with low zonal wind speeds in the lower stratosphere at an altitude of ~20 km. The zonal wind direction above the QZWL layer is opposite to that below the QZWL layer and the north –south wind component is small. The atmospheric wind field near the stratospheric QZWL is an important factor affecting the flight altitude and dynamic control of stratospheric airships. It is therefore necessary to study the stratospheric QZWL to provide better environmental information for these aircraft. High-resolution radiosonde data were used to analyze the characteristics of the stratospheric QZWL over Korla, Xinjiang Province, China. A weak wind layer in which the wind direction suddenly reversed from westerly to easterly was observed at ~20 km in the lower stratosphere, characteristic of the stratospheric QZWL. The Weather Research and Forecasting model was used to simulate the profiles of the horizontal wind speed and direction over Korla. The forcing effect of each diagnostic term in the equation on the zonal wind speed was analyzed. The results showed that the advection term was the dominant factor forcing the zonal wind speed. The wave term had a secondary forcing role, although the forcing effect of the wave term on the zonal wind speed was significant in some regions.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
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
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
In this paper, a new class of rings, called FIC rings, is introduced for studying quasi-zero-divisor graphs of rings. Let R be a ring. The quasi-zero-divisor graph of R, denoted by Г＊（R）, is a directed graph defin...In this paper, a new class of rings, called FIC rings, is introduced for studying quasi-zero-divisor graphs of rings. Let R be a ring. The quasi-zero-divisor graph of R, denoted by Г＊（R）, is a directed graph defined on its nonzero quasi-zero-divisors, where there is an arc from a vertex x to another vertex y if and only if xRy = 0. We show that the following three conditions on an FIC ring R are equivalent： （1） χ（R） is finite; （2） ω（R） is finite; （3） Nil＊ R is finite where Nil.R equals the finite intersection of prime ideals. Furthermore, we also completely determine the connectedness, the diameter and the girth of Г＊ （R）.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
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
Vibration isolation for low frequency excitation and the power supply for low power monitoring sensors are important issues in bridge engineering.The main problem is how to effectively combine the vibration isolator w...Vibration isolation for low frequency excitation and the power supply for low power monitoring sensors are important issues in bridge engineering.The main problem is how to effectively combine the vibration isolator with the energy harvester to form a multi-functional structure.In this paper,a system called quasi-zero stiffness energy harvesting isolator(QZS-EHI)with triple negative stiffness(TNS)is proposed.The TNS structure consists of linear springs,rigid links,sliders,and ring permanent magnets.Newton’s second law and Kirchhoff’s law construct dynamic equations of the QZS-EHI,and a comparison is made to contrast it with other QZS and linear isolators.The comparison field includes the QZS range,amplitude-frequency relationship,force transmissibility,and energy harvested power.The isolator can be applied to many engineering fields such as bridges,automobiles,and railway transportation.This paper selects bridge engineering as the main field for the dynamic analysis of this system.Considering the multi-span beam bridge,this paper compares different situations including the bridge with QZS-EHI support,with linear stiffness isolator support,and with single beam support.All results show that the QZS-EHI is not only better than the traditional isolator with linear stiffness under both harmonic and stochastic excitation,but also better than some QZS isolators with double or single negative stiffness in bridge vibration isolation and energy harvesting.Theoretical analysis is verified to correspond to the simulation analysis,which means the proposed QZS-EHI has practical application value.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
Gravity compensation refers to the creation of a constant supporting force to fully or partly counteract the gravitational force for ground verification to simulate the spacecraft dynamics in outer space with zero-or ...Gravity compensation refers to the creation of a constant supporting force to fully or partly counteract the gravitational force for ground verification to simulate the spacecraft dynamics in outer space with zero-or micro-gravity. Gravity compensation is usually implemented via a very low stiffness suspension/supporting unit, and a servo system in series is adopted to extend the simulation range to hundreds of millimeters. The error of suspension force can be up to tens of Newton due to the contact/friction in the suspension/supporting unit and the error of the force/pressure sensor. It has become a bottleneck for the ground verification of spacecraft guidance, navigation, and control systems with extreme requirements, such as tons of payload and fine thrust in sub-Newtons. In this article, a novel gravity compensation method characterized by quasi-zero stiffness plus quasi-zero deformation(QZS-QZD) is proposed. A magnetic negative stiffness spring in parallel with positive springs and aerostatic bearing is adopted to form a QZS supporting unit, and disturbance forces, such as contact or friction, can be eliminated. The deformation of the QZS supporting unit is measured via a displacement sensor, and the QZD control strategy is applied to guarantee the force error of gravity compensation to be less than sub-newtons and irrelevant to the payload. The principle of gravity compensation with QZS-QZD is analyzed, and performance tests on a prototype are carried out. The results show that when the spacecraft moves smoothly, the absolute force error is less than 0.5 N, the relative error of gravity compensation is less than 0.1%, and when collisions with other objects occur, the relative errors are 0.32% and 0.65%. The proposed method can significantly improve the gravity compensation accuracy in comparison with conventional approaches.展开更多
In this paper, an archetypal aseismic system is proposed with 2-degree of freedom based on a smooth and discontinuous(SD)oscillator to avoid the failure of electric power system under the complex excitation of seismic...In this paper, an archetypal aseismic system is proposed with 2-degree of freedom based on a smooth and discontinuous(SD)oscillator to avoid the failure of electric power system under the complex excitation of seismic waves. This model comprises two vibration isolation units for the orthogonal horizontal directions, and each of them admits the stable quasi-zero stiffness(SQZS)with a pair of inclined linear elastic springs. The equation of motion is formulated by using Lagrange equation, and the SQZS condition is obtained by optimizing the parameters of the system. The analysis shows that the system behaves a remarkable vibration isolation performance with low resonant frequency and a large stroke of SQZS interval. The experimental investigations are carried out to show a high sonsistency with the theoretical results, which demonstrates the improvement of aseismic behavior of the proposed model under the seismic wave.展开更多
Quasi-zero stiffness(QZS) device is widely studied for their better performance in low-frequency and micro-vibration isolation due to the high-static and low-dynamic(HSLD) stiffness characteristics.The previous QZS is...Quasi-zero stiffness(QZS) device is widely studied for their better performance in low-frequency and micro-vibration isolation due to the high-static and low-dynamic(HSLD) stiffness characteristics.The previous QZS isolator with determined parameters is not suitable for variable isolated mass.In this study,a novel compound regulative quasi-zero stiffness air spring(CRQSAS)has been proposed and designed by introducing a bidirectional regulator for the horizontal air springs.The CRQSAS could change the quasi-zero region depending on the payload.To identify the parameters of the convoluted air spring(CAS) and novel rubber air spring(NRAS),the air spring testing system is established.The stiffness functions of air springs are obtained by the multi-parameter fitting method.According to the structure of the CRQSAS,the dynamic model of the system is analyzed and simplified by Taylor Expansion.The harmonic balance method(HBM) is applied to calculate the frequency response and absolute displacement transmissibility.An experimental prototype has been set up to verify the theoretical model and simulation.Compared with the single NRAS,CRQSAS performs better in low-frequency and micro-amplitude vibration.The research proves that CRQSAS is a passive device widely applied for improving isolation precision under low-frequency vibration.展开更多
基金supported by the National Natural Science Foundation of China(52332006)the National Key Research and Development Program of China(2022YFB380600 and 2023YFB3811401)+1 种基金the China Postdoctoral Science Foundation(2022M721850)Southwest United Graduate School Research Program(202302AO370008)。
文摘Quasi-zero-stiffness(QZS)metamaterials have attracted significant interest for application in low-frequency vibration isolation.However,previous work has been limited by the design mechanism of QZS metamaterials,as it is still difficult to achieve a simplified structure suitable for practical engineering applications.Here,we introduce a class of programmable QZS metamaterials and a novel design mechanism that address this long-standing difficulty.The proposed QZS metamaterials are formed by an array of representative unit cells(RUCs)with the expected QZS features,where the QZS features of the RUC are tailored by means of a structural bionic mechanism.In our experiments,we validate the QZS features exhibited by the RUCs,the programmable QZS behavior,and the potential promising applications of these programmable QZS metamaterials in low-frequency vibration isolation.The obtained results could inspire a new class of programmable QZS metamaterials for low-frequency vibration isolation in current and future mechanical and other engineering applications.
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.
基金supported in part by National Key R&D Program of China under Grant 2024YFB4708600National Natural Science Foundation of China under Grant 52305304+3 种基金Jilin Youth Growth Technology Project under Grant 20230508147RCthe Science and Technology Research Project of Jilin Provincial Education Department(No.JJKH20231193KJ)supported in part by the National Natural Science Foundation of China under Grant 52021003 and Grant 52205565in part by the Natural Science Foundation of Jilin Province under Grant 20210101053JC.
文摘Traditional linear vibration isolators struggle to combine high load-bearing capacity with low-frequency vibration isolation, whereas nonlinear metastructure isolators can effectively fulfill both functions. This paper draws inspiration from the Quasi-Zero Stiffness (QZS) characteristics resulting from the buckling deformation of beams, and proposes a gear-based QZS structure by arranging beams in a circular array. We investigated the static mechanical behavior under different structural parameters, loading angles, and gear combinations through experiments and simulations, and demonstrated the mechanical performances could be effectively programmed. Subsequent vibration isolation tests on the double gears prove superior vibration isolation performance at low frequency while maintaining high load-bearing capacities. Additionally, a key contribution of our work is the development of a mathematical model to characterize the buckling behavior of the unit beam within the gear structure, with its accuracy validated through finite element analysis and experimental results. The gear’s modulus, number of teeth, and pressure angle are selected according to standard series, allowing the gear can be seamlessly integrated into existing mechanical systems in critical fields such as aerospace, military, and etc.
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Project supported by the National Natural Science Foundation of China(No.U23A2066)the Liaoning Revitalization Talents Program of China(No.XLYC2202032)。
文摘Bionic X-shaped vibration isolators have been widely employed in aerospace and other industrial fields,but the stiffness properties of classic X-shaped structures limit the vibration isolation ability for low frequencies.An innovative bionic quasi-zero stiffness(QZS)vibration isolator(BQZSVI),which can broaden the QZS range of a classic X-shaped isolator and can bring it closer to the equilibrium position,is proposed.The BQZSVI consists of an X-shaped structure as the bone fabric of lower limbs and a nonlinear magnetic loop device simulating the leg muscle.Based on static calculation,the stiffness characteristic of the structure is confirmed.The governing equations of motion of the BQZSVI structure are established in the framework of the Lagrange equation,and the harmonic balance method(HBM)is adopted to obtain the transmissibility responses.The results show that the BQZSVI can provide a more accessible and broader range of QZS.In the dynamic manifestation,the introduction of the BQZSVI can reduce the amplitude of a classic X-shaped vibration isolator by 65.7%,and bring down the initial vibration isolation frequency from 7.43 Hz to 2.39 Hz.In addition,a BQZSVI prototype is designed and fabricated,and the exactitude of the theoretical analysis method is proven by means of experiments.
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 the National Natural Science Foundation of China(Grants 11832009 and 11672104)the Chair Professor of Lotus Scholars Program in Hunan province(Grants XJT2015408)。
文摘Vibration reduction has always been one of hot and important topics in mechanical engineering,especially for the special measurement instrument.In this paper,a novel limb-inspired bionic structure is proposed to generate negative stiffness and design a new quasi-zero stiffness isolator via torsion springs,distinguishing from the existing tension spring structures in the literature.The nonlinear mathematical model of the proposed structure is developed and the corresponding dynamic properties are further investigated by using the Harmonic Balance method and ADAMS verification.To evaluate the vibration isolation performance,typical three-springs quasi-zero stiffness(TS QZS)system is selected to compare with the proposed bionic structure.And the graphical processing unit(GPU)parallel technology is applied to perform necessary two-parameter analyses,providing more insights into the effects of parameters on the transmissibility.It is shown that the proposed structure can show advantages over the typical TS QZS system in a wider vibration isolation range for harmonic excitation case and shorter decay time for the impact excitation case.
基金Supported by National Natural Science Foundation of China(Grant No.51875256)Open Platform Fund of Hunan Institute of Technology of China(Grant No.KFA20009)Hong Kong,Macao and Taiwan Science and Technology Cooperation Project in Jiangsu Province of China(Grant No.BZ2020050)。
文摘To improve the vibration isolation performance of suspensions,various new structural forms of suspensions have been proposed.However,there is uncertainty in these new structure suspensions,so the deterministic research cannot refect the performance of the suspension under actual operating conditions.In this paper,a quasi-zero stifness isolator is used in automotive suspensions to form a new suspension−quasi-zero stifness air suspension(QZSAS).Due to the strong nonlinearity and structural complexity of quasi-zero stifness suspensions,changes in structural parameters may cause dramatic changes in suspension performance,so it is of practical importance to study the efect of structural parameter uncertainty on the suspension performance.In order to solve this problem,three suspension structural parameters d_(0),L_(0) and Pc_(0) are selected as random variables,and the polynomial chaos expansion(PCE)theory is used to solve the suspension performance parameters.The sensitivity of the performance parameters to diferent structural parameters was discussed and analyzed in the frequency domain.Furthermore,a multi-objective optimization of the structural parameters d_(0),L_(0) and Pc_(0) of QZSAS was performed with the mean and variance of the root-mean-square(RMS)acceleration values as the optimization objectives.The optimization results show that there is an improvement of about 8%−1_(0)%in the mean value and about 4_(0)%−55%in the standard deviation of acceleration(RMS)values.This paper verifes the feasibility of the PCE method for solving the uncertainty problem of complex nonlinear systems,which provide a reference for the future structural design and optimization of such suspension systems.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA17010105)
文摘The stratospheric quasi-zero wind layer (QZWL) is a transition region with low zonal wind speeds in the lower stratosphere at an altitude of ~20 km. The zonal wind direction above the QZWL layer is opposite to that below the QZWL layer and the north –south wind component is small. The atmospheric wind field near the stratospheric QZWL is an important factor affecting the flight altitude and dynamic control of stratospheric airships. It is therefore necessary to study the stratospheric QZWL to provide better environmental information for these aircraft. High-resolution radiosonde data were used to analyze the characteristics of the stratospheric QZWL over Korla, Xinjiang Province, China. A weak wind layer in which the wind direction suddenly reversed from westerly to easterly was observed at ~20 km in the lower stratosphere, characteristic of the stratospheric QZWL. The Weather Research and Forecasting model was used to simulate the profiles of the horizontal wind speed and direction over Korla. The forcing effect of each diagnostic term in the equation on the zonal wind speed was analyzed. The results showed that the advection term was the dominant factor forcing the zonal wind speed. The wave term had a secondary forcing role, although the forcing effect of the wave term on the zonal wind speed was significant in some regions.
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 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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1137134311161006+4 种基金1166101411171142)the Guangxi Science Research and Technology Development Project(Grant No.1599005-2-13)the Scientic Research Fund of Guangxi Education Department(Grant No.KY2015ZD075)the Natural Science Foundation of Guangxi(Grant No.2016GXSFDA380017)
文摘In this paper, a new class of rings, called FIC rings, is introduced for studying quasi-zero-divisor graphs of rings. Let R be a ring. The quasi-zero-divisor graph of R, denoted by Г＊（R）, is a directed graph defined on its nonzero quasi-zero-divisors, where there is an arc from a vertex x to another vertex y if and only if xRy = 0. We show that the following three conditions on an FIC ring R are equivalent： （1） χ（R） is finite; （2） ω（R） is finite; （3） Nil＊ R is finite where Nil.R equals the finite intersection of prime ideals. Furthermore, we also completely determine the connectedness, the diameter and the girth of Г＊ （R）.
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.
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 the National Natural Science Foundation of China(Grant No.12272293)Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2022A1515010967 and 2023A1515012821).
文摘Vibration isolation for low frequency excitation and the power supply for low power monitoring sensors are important issues in bridge engineering.The main problem is how to effectively combine the vibration isolator with the energy harvester to form a multi-functional structure.In this paper,a system called quasi-zero stiffness energy harvesting isolator(QZS-EHI)with triple negative stiffness(TNS)is proposed.The TNS structure consists of linear springs,rigid links,sliders,and ring permanent magnets.Newton’s second law and Kirchhoff’s law construct dynamic equations of the QZS-EHI,and a comparison is made to contrast it with other QZS and linear isolators.The comparison field includes the QZS range,amplitude-frequency relationship,force transmissibility,and energy harvested power.The isolator can be applied to many engineering fields such as bridges,automobiles,and railway transportation.This paper selects bridge engineering as the main field for the dynamic analysis of this system.Considering the multi-span beam bridge,this paper compares different situations including the bridge with QZS-EHI support,with linear stiffness isolator support,and with single beam support.All results show that the QZS-EHI is not only better than the traditional isolator with linear stiffness under both harmonic and stochastic excitation,but also better than some QZS isolators with double or single negative stiffness in bridge vibration isolation and energy harvesting.Theoretical analysis is verified to correspond to the simulation analysis,which means the proposed QZS-EHI has practical application value.
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 Key R&D Program of China (Grant No. 2020YFB2007601)the National Natural Science Foundation of China (Grant No. 52075193)the National Major Science and Technology Projects of China (Grant No. 2017ZX02101007-002)。
文摘Gravity compensation refers to the creation of a constant supporting force to fully or partly counteract the gravitational force for ground verification to simulate the spacecraft dynamics in outer space with zero-or micro-gravity. Gravity compensation is usually implemented via a very low stiffness suspension/supporting unit, and a servo system in series is adopted to extend the simulation range to hundreds of millimeters. The error of suspension force can be up to tens of Newton due to the contact/friction in the suspension/supporting unit and the error of the force/pressure sensor. It has become a bottleneck for the ground verification of spacecraft guidance, navigation, and control systems with extreme requirements, such as tons of payload and fine thrust in sub-Newtons. In this article, a novel gravity compensation method characterized by quasi-zero stiffness plus quasi-zero deformation(QZS-QZD) is proposed. A magnetic negative stiffness spring in parallel with positive springs and aerostatic bearing is adopted to form a QZS supporting unit, and disturbance forces, such as contact or friction, can be eliminated. The deformation of the QZS supporting unit is measured via a displacement sensor, and the QZD control strategy is applied to guarantee the force error of gravity compensation to be less than sub-newtons and irrelevant to the payload. The principle of gravity compensation with QZS-QZD is analyzed, and performance tests on a prototype are carried out. The results show that when the spacecraft moves smoothly, the absolute force error is less than 0.5 N, the relative error of gravity compensation is less than 0.1%, and when collisions with other objects occur, the relative errors are 0.32% and 0.65%. The proposed method can significantly improve the gravity compensation accuracy in comparison with conventional approaches.
基金the financial support from the National Natural Science Foundation of China(Grant Nos.11572096,11732006)
文摘In this paper, an archetypal aseismic system is proposed with 2-degree of freedom based on a smooth and discontinuous(SD)oscillator to avoid the failure of electric power system under the complex excitation of seismic waves. This model comprises two vibration isolation units for the orthogonal horizontal directions, and each of them admits the stable quasi-zero stiffness(SQZS)with a pair of inclined linear elastic springs. The equation of motion is formulated by using Lagrange equation, and the SQZS condition is obtained by optimizing the parameters of the system. The analysis shows that the system behaves a remarkable vibration isolation performance with low resonant frequency and a large stroke of SQZS interval. The experimental investigations are carried out to show a high sonsistency with the theoretical results, which demonstrates the improvement of aseismic behavior of the proposed model under the seismic wave.
基金supported by the National Key Research and Development Project (Grant No.2021YFC0122502)the National Natural Science Foundation of China (Grant Nos.52205043 and 52275043)。
文摘Quasi-zero stiffness(QZS) device is widely studied for their better performance in low-frequency and micro-vibration isolation due to the high-static and low-dynamic(HSLD) stiffness characteristics.The previous QZS isolator with determined parameters is not suitable for variable isolated mass.In this study,a novel compound regulative quasi-zero stiffness air spring(CRQSAS)has been proposed and designed by introducing a bidirectional regulator for the horizontal air springs.The CRQSAS could change the quasi-zero region depending on the payload.To identify the parameters of the convoluted air spring(CAS) and novel rubber air spring(NRAS),the air spring testing system is established.The stiffness functions of air springs are obtained by the multi-parameter fitting method.According to the structure of the CRQSAS,the dynamic model of the system is analyzed and simplified by Taylor Expansion.The harmonic balance method(HBM) is applied to calculate the frequency response and absolute displacement transmissibility.An experimental prototype has been set up to verify the theoretical model and simulation.Compared with the single NRAS,CRQSAS performs better in low-frequency and micro-amplitude vibration.The research proves that CRQSAS is a passive device widely applied for improving isolation precision under low-frequency vibration.
