Nonlinear Characteristic Analysis of Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension System:A Theoretical and Experimental Study

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.

A vibration isolator with a controllable quasi-zero stiffness region based on nonlinear force design

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.

Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine

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.

Design and Analysis of a Horizontal Quasi-Zero Stiffness Vibration Isolator by Combining Rolling-Ball and Disk Springs in Parallel

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.

Isolation performances and optimization of triple quasi-zero stiffness isolators

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.

Multi-layer quasi-zero-stiffness meta-structure for high-efficiency vibration isolation at low frequency

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.

A quasi-zero stiffness energy harvesting isolator with triple negative stiffness

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.

Novel modular quasi-zero stiffness vibration isolator with high linearity and integrated fluid damping

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.

Three-magnet-ring quasi-zero stiffness isolator for low-frequency vibration isolation

A three-magnet-ring quasi-zero stiffness(QZS-TMR)isolator is designed to solve the problem of low-frequency vibration isolation in the vertical direction of precision equipment.QZS-TMR has both positive and negative stiffness structures.The positive stiffness structure consists of two mutually repelling magnetic rings and the negative stiffness structure consists of two magnetic rings nested within each other.By modulating the relative distance between positive and negative stiffness structures,the isolator can have QZS characteristics.Compared with other QZS isolators,the QZS-TMR is compact and easy to manufacture.In addition,the working load of QZS-TMR can be flexibly adjusted by varying the radial widths of the inner magnetic ring.In this paper,the static analysis of QZS-TMR is carried out to guide the design,and the low-frequency vibration isolation performance is studied.In addition,the experimental prototype of QZS-TMR is designed and manufactured.The static and vibration isolation experiments are carried out on the prototype.The results show that the initial vibration isolation frequency of the experimental prototype is about 4 Hz.The results show an excellent low-frequency vibration isolation effect,which is consistent with the theoretical research.This paper introduces a new approach to the design of the QZS isolator.

Dynamic frequency response characteristics of a compound regulative quasi-zero stiffness air spring system

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.

Cyclic shear behavior of en-echelon joints under constant normal stiffness conditions

To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)conditions.We analyzed the evolution of shear stress,normal stress,stress path,dilatancy characteristics,and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles.The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle,with the shear strength at a positive angle exceeding that at a negative angle during shear cycles.As the number of cycles increases,the shear strength decreases rapidly,and the difference between the varying angles gradually decreases.Dilation occurs in the early shear cycles(1 and 2),while contraction is the main feature in later cycles(310).The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles.The joint angle determines the asperities on the rupture surfaces and the block size,and thus determines the subsequent shear failure mode(block crushing and asperity degradation).At positive angles,block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles.Therefore,the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.

A low-frequency pure metal metamaterial absorber with continuously tunable stiffness

To address the incompatibility between high environmental adaptability and deep subwavelength characteristics in conventional local resonance metamaterials,and overcome the deficiencies in the stability of existing active control techniques for band gaps,this paper proposes a design method of pure metal vibration damping metamaterial with continuously tunable stiffness for wideband elastic wave absorption.We design a dual-helix narrow-slit pure metal metamaterial unit,which possesses the triple advantage of high spatial compactness,low stiffness characteristics,and high structural stability,enabling the opening of elastic flexural band gaps in the low-frequency range.Similar to the principle of a sliding rheostat,the introduction of continuously sliding plug-ins into the helical slits enables the continuous variation of the stiffness of the metamaterial unit,achieving a continuously tunable band gap effect.This successfully extends the effective band gap by more than ten times.The experimental results indicate that this metamaterial unit can be used as an additional vibration absorber to absorb the low-frequency vibration energy effectively.Furthermore,it advances the metamaterial absorbers from a purely passive narrowband design to a wideband tunable one.The pure metal double-helix metamaterials retain the subwavelength properties of metamaterials and are suitable for deployment in harsh environments.Simultaneously,by adjusting its stiffness,it substantially broadens the effective band gap range,presenting promising potential applications in various mechanical equipment operating under adverse conditions.

Evaluation on Configuration Stiffness of Overconstrained 2R1T Parallel Mechanisms

Currently,two rotations and one translation(2R1T)three-degree-of-freedom(DOF)parallel mechanisms(PMs)are widely applied in five-DOF hybrid machining robots.However,there is a lack of an effective method to evaluate the configuration stiffness of mechanisms during the mechanism design stage.It is a challenge to select appropriate 2R1T PMs with excellent stiffness performance during the design stage.Considering the operational status of 2R1T PMs,the bending and torsional stiffness are considered as indices to evaluate PMs'configuration stiffness.Subsequently,a specific method is proposed to calculate these stiffness indices.Initially,the various types of structural and driving stiffness for each branch are assessed and their specific values defined.Subsequently,a rigid-flexible coupled force model for the over-constrained 2R1T PM is established,and the proposed evaluation method is used to analyze the configuration stiffness of the five 2R1T PMs in the entire workspace.Finally,the driving force and constraint force of each branch in the whole working space are calculated to further elucidate the stiffness evaluating results by using the proposed method above.The obtained results demonstrate that the bending and torsional stiffness of the 2RPU/UPR/RPR mechanism along the x and y-directions are larger than the other four mechanisms.

Stiffness-tunable biomaterials provide a good extracellular matrix environment for axon growth and regeneration

Neuronal growth, extension, branching, and formation of neural networks are markedly influenced by the extracellular matrix—a complex network composed of proteins and carbohydrates secreted by cells. In addition to providing physical support for cells, the extracellular matrix also conveys critical mechanical stiffness cues. During the development of the nervous system, extracellular matrix stiffness plays a central role in guiding neuronal growth, particularly in the context of axonal extension, which is crucial for the formation of neural networks. In neural tissue engineering, manipulation of biomaterial stiffness is a promising strategy to provide a permissive environment for the repair and regeneration of injured nervous tissue. Recent research has fine-tuned synthetic biomaterials to fabricate scaffolds that closely replicate the stiffness profiles observed in the nervous system. In this review, we highlight the molecular mechanisms by which extracellular matrix stiffness regulates axonal growth and regeneration. We highlight the progress made in the development of stiffness-tunable biomaterials to emulate in vivo extracellular matrix environments, with an emphasis on their application in neural repair and regeneration, along with a discussion of the current limitations and future prospects. The exploration and optimization of the stiffness-tunable biomaterials has the potential to markedly advance the development of neural tissue engineering.

Iterative Subregion Correction Preconditioners with Adaptive Tolerance for Problems with Geometrically Localized Stiffness

We present a class of preconditioners for the linear systems resulting from a finite element or discontinuous Galerkin discretizations of advection-dominated problems.These preconditioners are designed to treat the case of geometrically localized stiffness,where the convergence rates of iterative methods are degraded in a localized subregion of the mesh.Slower convergence may be caused by a number of factors,including the mesh size,anisotropy,highly variable coefficients,and more challenging physics.The approach taken in this work is to correct well-known preconditioners such as the block Jacobi and the block incomplete LU(ILU)with an adaptive inner subregion iteration.The goal of these preconditioners is to reduce the number of costly global iterations by accelerating the convergence in the stiff region by iterating on the less expensive reduced problem.The tolerance for the inner iteration is adaptively chosen to minimize subregion-local work while guaranteeing global convergence rates.We present analysis showing that the convergence of these preconditioners,even when combined with an adaptively selected tolerance,is independent of discretization parameters(e.g.,the mesh size and diffusion coefficient)in the subregion.We demonstrate significant performance improvements over black-box preconditioners when applied to several model convection-diffusion problems.Finally,we present performance results of several variations of iterative subregion correction preconditioners applied to the Reynolds number 2.25×10^(6)fluid flow over the NACA 0012 airfoil,as well as massively separated flow at 30°angle of attack.

Theoretical and experimental investigations on an X-shaped vibration isolator with active controlled variable stiffness

A novel X-shaped variable stiffness vibration isolator(X-VSVI)is proposed.The Runge-Kutta method,harmonic balance method,and wavelet transform spectra are introduced to evaluate the performance of the X-VSVI under various excitations.The layer number,the installation angle of the X-shaped structure,the stiffness,and the active control parameters are systematically analyzed.In addition,a prototype of the X-VSVI is manufactured,and vibration tests are carried out.The results show that the proposed X-VSVI has a superior adaptability to that of a traditional X-shaped mechanism,and shows excellent vibration isolation performance in response to different amplitudes and forms of excitations.Moreover,the vibration isolation efficiency of the device can be improved by appropriate adjustment of parameters.

Performance of composite foundations with different load transfer platforms and substratum stiffness over silty clay

The semi-rigid pile-supported composite foundation is widely used in highway projects due to its effectiveness in increasing the bearing capacity and stability of foundations.It is crucial to understand the stress distribution across the embankment width and the behaviour of unreinforced foundations.Thus,five centrifuge tests were conducted to examine the bearing and deformation behaviours of NPRS(Non-Connected Piled Raft Systems)and GRPS(GeosyntheticReinforced Pile-Supported systems)with varying substratum stiffness,then a comparative analysis was conducted on embankment settlement,pressures underneath the embankments,and axial forces along the piles.The results indicated that greater substratum stiffness correlates with reduced settlement and deformation at various depths.Deformation occurring 5 meters from the embankment toe includes settlement in NPRS and upward movement in GRPS.The potential sliding surface is primarily located within the embankment in NPRS,whereas it may extend through both the embankment and foundation in GRPS.The pile-soil stress ratio and efficiency in NPRS are higher than in GRPS across the embankment.The axial force borne by end-bearing piles is significantly greater than that by floating piles.As the buried depth increases,the axial force in GRPS initially rises then declines,whereas in NPRS,it remains relatively constant within a certain range before decreasing.This study aids in assessing the applicability of composite foundations in complex railway environments and provides a reference for procedural measures under similar conditions.

Negative Stiffness Mechanism on An Asymmetric Wave Energy Converter by Using A Weakly Nonlinear Potential Model

Salter's duck,an asymmetrical wave energy converter(WEC)device,showed high efficiency in extracting energy from 2D regular waves in the past;yet,challenges remain for fluctuating wave conditions.These can potentially be addressed by adopting a negative stiffness mechanism(NSM)in WEC devices to enhance system efficiency,even in highly nonlinear and steep 3D waves.A weakly nonlinear model was developed which incorporated a nonlinear restoring moment and NSM into the linear formulations and was applied to an asymmetric WEC using a time domain potential flow model.The model was initially validated by comparing it with published experimental and numerical computational fluid dynamics results.The current results were in good agreement with the published results.It was found that the energy extraction increased in the range of 6%to 17%during the evaluation of the effectiveness of the NSM in regular waves.Under irregular wave conditions,specifically at the design wave conditions for the selected test site,the energy extraction increased by 2.4%,with annual energy production increments of approximately 0.8MWh.The findings highlight the potential of NSM in enhancing the performance of asymmetric WEC devices,indicating more efficient energy extraction under various wave conditions.

Ilizarov technique for treating elbow stiffness caused by myositis ossificans:A case report

BACKGROUND Myositis ossificans(MO)is a rare disease involving the formation of bone outside the musculoskeletal system.While surgical intervention is the main treatment approach,preventing recurrence and standardized rehabilitation are also crucial.Here,we present a surgical strategy to prevent the recurrence of MO.CASE SUMMARY A 28-year-old female patient was admitted for the first time for a comminuted fracture of the left olecranon.However,incorrect postoperative rehabilitation resulted in the development of elbow joint stiffness with ectopic ossification,causing a loss of normal range of motion.The patient was diagnosed with MO based on physical examination,X-ray findings,and clinical presentation.We devised a surgical strategy to remove MO,followed by fixation with an Ilizarov frame,and implemented a scientifically reasonable rehabilitation plan.The surgery lasted for 3 h with an estimated blood loss of 45 mL.A drainage tube was placed after surgery,and fluid was aspirated through ultrasound-guided puncture.The patient experienced a significant reduction in joint stiffness after surgery.In the final follow-up at 9 mouths,there was evident improvement in the range of motion of the elbow joint,and no other symptoms were reported.CONCLUSION The Ilizarov frame is an advantageous surgical technique for facilitating rehabilitation after MO removal.It offers benefits such as passive recovery,individualized treatment,and prompt recovery.

Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.