Quasi-zero Stiffness Research Articles

Isolation performances and optimization of triple quasi-zero stiffness isolators

Isolation performances and optimization of triple quasi-zero stiffness isolators

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. However, 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 quasi-zero stiffness energy harvesting isolator with triple negative stiffness

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

Stochastic evaluation of quasi-zero stiffness magnetic spring using a reluctance-corrected analytical model

—In state of the art high-precision motion systems, which utilize magnetic levitation, a quasi-zero stiffness gravity compensation is one of the essentials to improve dynamic performance, eliminate position dependency and thus simplify controller design. Special configurations of permanent magnets, such as Halbach magnet arrays, can realize magnetic levitation as a form of magnetic spring. However, unlike conventional permanent magnet machines with large stiffness, the quasi-zero stiffness magnetic spring requires higher modeling accuracy for force estimation, which is affected by the nonlinear reluctance effect of permanent magnets. In this study, we propose an accurate magnetic modeling method for the quasi-zero stiffness magnetic spring. By correcting the reluctance effect of magnets, the proposed magnetic model achieves superior accuracy estimating levitation force and stiffness to the conventional surface current model. Using the reluctance-corrected magnetic model, tolerance analysis was performed to identify dominant geometric parameters affecting the uncertainty of the Halbach array magnetic spring performance. A Monte-Carlo simulation was used to estimate the overall tolerance of magnetic forces and stiffness. The experimental results fit in the tolerances.

Effect of disk-to-disk variations on the nonlinear static characteristics and stability regimes of coned disk spring stacks: Experimental and computational studies of quasi-zero-stiffness isolators

In this study, we introduce a novel approach to creating a Quasi-Zero Stiffness (QZS) isolator using off-the-shelf coned disk springs with a unique stack. These springs are affordable, compact, and can be adapted for a broad spectrum of force requirements, enabling the achievement of the QZS effect using a solitary component, thereby eliminating the need to balance the positive and negative stiffness elements. To address the issue of the limited displacement range offered by a single coned spring, the solution involves layering multiple disk springs with rigid spacers. Nonetheless, the nonlinear force–deflection behavior is significantly affected by manufacturing-driven geometric variability due to inherent differences from one disk spring to another. This aspect of variability has been overlooked by previous researchers, who have operated under the assumption that all disks in a stack are identical. This research delves into how variations in the disk springs’ geometry impact the nonlinear static behavior of the QZS stacks, employing both experimental and computational techniques. We illustrate the stability conditions and pinpoint the occurrences of buckling and snap-through events. Computational model for the multi-disk engineered stack is experimentally validated. Finally, we explore the QZS isolator design approaches that would take into account these geometric variations.

Generative quasi-zero stiffness paradigm for vibration isolation by constraining the constant force with hardening boundaries

Quasi-zero stiffness (QZS) isolators are widely used to mitigate the low-frequency vibration. This paper proposes a new QZS paradigm for vibration isolation utilizing constant force with hardening boundaries (CFHB). Different from the conventional parallel connection of positive and negative stiffness elements, the CFHB directly exhibits the QZS characteristic which is generated when the uniform magnetic field is converted to a non-uniform one. Therefore, it avoids complex assembly and material deformation, and eschews the reliability issues related to stiffness combination. Concretely, the radially magnetized shaft has a uniform area in the middle part which can be distorted by a coaxial sleeve made of high permeability material. A constant magnetic force is generated in this process. Two hardening boundaries formed by two pair of repulsive magnets are applied to constrain the QZS stroke and maintains the working position. The shaft's magnetic field is studied to clarify the filed distribution, and the distortion by the sleeve is simulated by finite element analysis (FEA). The force-displacement relationship of the case study is proven to be continuous and fitted by a polynomial form. The influence of dimension parameters on the performance of vibration isolator is systematically investigated to guide the design. Dynamic differential equation considering Coulomb damping and viscous damping is established and solved applying the Runge-Kutta Method (RKM) to obtain the vibration response. A prototype is fabricated to experimentally validate its performance, demonstrating the QZS properties in quasi-static calibration and the vibration isolation effect under the frequency sweep and periodic excitations. The generative QZS offers a new paradigm with a simple structure, suggesting its substantial potential for practical deployment.

A concave X-shaped structure supported by variable pitch springs for low-frequency vibration isolation

Based on the known X-shaped structure, a concave X-shaped structure (CXSS) featuring custom-designed variable pitch springs (VPS) is proposed. This design aims to enhance the displacement range of the quasi-zero stiffness (QZS) system and improve its performance in isolating low-frequency vibrations. The CXSS is obtained by merging two semi-X-shaped structures. The negative stiffness property of the concave structure can be improved by utilizing the motion limitations of the mechanical structure. Of particular concern is the VPS, it can provide nonlinear restoring force and variable stiffness by self-adjusting the effective number of coils. This special spring is suitable to neutralize the negative stiffness of the concave structure, enabling a wider range of QZS properties than linear springs and magnets. The average error between the practical and theoretical restoring force of the VPS is less than 10 %. Based on a special compression coefficient, the objective-load design method (OLDM) is proposed to obtain the stiffness conditions implementing QZS properties against rated mass. The stiffness obtained by the OLDM is considerably accurate. Under this condition, the vibration transmissibility is about 0.45 at 3.5 Hz and 0.1 at 14 Hz, which is lower than that of the unmatched load and stiffness coefficients. Compared with the X-shaped structure, the proposed structure has better low-frequency vibration isolation performance with a natural frequency of about 2 Hz. The vibration transmissibility is about 0.2 at 5 Hz and is about 0.1 at 10 Hz. Pulse excitations with an amplitude of 16 g can be attenuated to about 0.51 g through the CXSS compensated by VPS. It is convenient and efficient to implement QZS properties using the VPS to compensate negative stiffness.

Double roller negative stiffness mechanism seat suspension optimization design and vibration analysis

To further improve the vibration isolation performance of automobile seat suspension and the riding comfort of automobiles, this paper uses the double roller negative stiffness mechanism (NSM) to calculate the seat suspension with quasi-zero stiffness (QZS) characteristics. The influence of the structural parameters on the QZS characteristics is simulated and analyzed, and the structural parameters are optimized by the orthogonal design method. The effectiveness of the optimization was verified by analyzing the dynamic response of the seat suspension system. The results show that the natural frequency of the vibration isolation system of the seat suspension decreases, the vibration isolation band widens after the introduction of the double roller NSM, and the vibration isolation effect is improved under low-frequency excitation.

Design of hyperbolic quasi-zero stiffness metastructures coupled with nonlinear stiffness for low-frequency vibration isolation

Quasi-zero stiffness (QZS) metastructures with simple structures exhibit a high low-frequency vibration isolation performance, but the bearing capacity and working regions are limited due to the linear positive stiffness elements. In this study, a novel hyperbolic QZS metastructure coupled with nonlinear stiffness is designed by combining a pair of cosine-shaped beams and arc-shaped beams for low-frequency vibration isolation. Finite element models (FEM) and experimental analysis are utilized to examine the static characteristics of the metastructure, revealing a wide QZS region and significant load-bearing capacity. The metastructure can achieve effective vibration isolation properties through reasonably designing the unit cells. The influence of geometrical parameters on the QZS region is investigated to optimize and realize desirable QZS features. The dynamic equation and response of the vibration isolation system are determined using the harmonic balance method. Moreover, the corresponding displacement transmissibility is confirmed by numerical simulation. The results of the dynamic sweep frequency experiment further verify the validity of the theoretical analysis model. The hyperbolic QZS metastructure system possesses good vibration isolation performance due to the introduction and compensation of a nonlinear positive stiffness arc beam element. The proposed hyperbolic QZS metastructure provides a significant route for the stiffness compensation of metastructures.

Dual-function of energy harvesting and vibration isolation via quasi-zero stiffness piezoelectric mechanism

Industry 4.0 realizes intelligent interconnection through the sensor group of the Internet of Things. A key challenge is to achieve the self-powering of sensors and stable operation of precision instruments. This paper introduces a dual-functional structure (VIPEH) integrating energy harvesting (EH) and vibration isolation (VI) based on the quasi-zero stiffness (QZS) piezoelectric mechanism. The paper analyzes the nonlinear statics of piezoelectric flexible beams under large deformations and conducts parametric analysis. A nonlinear dynamic model with electromechanical coupling was developed to investigate the impact of mechanical and electrical parameters on the system's dynamic bifurcation behavior, EH, and VI performance. Finally, an experimental setup is created to evaluate the VIPEH's characteristics. Sweep frequency excitation experiments demonstrate that the initial isolation frequency of VIPEH is lower than 1.4 Hz. The important thing is that VIPEH can still power the sensor based on the isolation frequency, and the output power of a single piezoelectric material can reach 3.19 mW. This not only enables the isolation of low-frequency vibrations but also presents a highly promising application for achieving self-powering in sensor clusters within the context of Industry 4.0 and the IoTs.

Vibration Isolation and Launch Performance Enhancement of the Spacecraft In-Orbit Launch Design Using the Nonlinear Dynamic Feature

This paper proposes a new spacecraft in-orbit launch design using a nonlinear configuration to utilize nonlinear dynamics for the enhancement of vibration isolation and launch performance. The in-orbit launch device has four springs, where the stroke directions of two springs are perpendicular to the launch direction so as to produce nonlinearity with negative stiffness for enhancing the launch velocity. The other two springs are designed to counterbalance the above negative stiffness when the launch outlet is shut down, leading to quasi-zero dynamic stiffness for vibration isolation enhancement. The dynamic equations of the in-orbit launch device for both the on- and off-launch are presented. Then the performance enhancement of both the vibration isolation and launch performance is thoroughly investigated via comparative study and parametric study. The resonance peak is reduced by 4.16 dB, the effective vibration isolation bandwidth is increased by 57%, and the launch speed is increased 1.64 times. This validates the performance improvement of the new launch device design and presents a useful guideline for application.

Dynamic analysis and performance evaluation of inerter fractional nonlinear quasi-zero stiffness isolator on a multi-span bridge under moving load

In this paper we propose a new vibration isolator system, which combines the advantages of a quasi-zero stiffness (QZS) isolator, a damper exhibiting fractional properties and an inerter, to reduce the vibrations of a multi-span continuous beam bridge excited by moving loads. The inerter produces a fictitious mass amplification effect to improve the controller performance and the fractional order takes into account the previous state of the viscoelastic material. After formulating the dynamics equation using beam theory, the amplitude response is determined analytically using the averaging method. The results obtained from the analytical study are validated using the direct numerical simulation method (Newton–Leipnik method). By comparing the isolation performance of the FQZS (fractional quasi-zero stiffness) isolator and the IFQZS (inerter fractional quasi-zero stiffness) isolator, it is shown that the addition of inertance can significantly suppress the tendency of the curve to slope to the right, allowing us to have a wider isolation frequency range on force transmissibility while improving the efficiency of the isolator. One also shows that increasing the fractional parameter contributes to a decrease in the vibration amplitude of the structure, the amplitude of the force transmitted and the area in which unstable solutions appear. However, beyond a certain value of the fractional parameter, we observe an increase in the latter. In order to further extend the study, bifurcation diagram, phase portrait, time history and power spectral density are explored.

A nonlinear low frequency quasi zero stiffness vibration isolator using double-arc flexible beams

There is an increasing demand for integrated small vibration isolators in precision sensing instruments and medical equipment. Therefore, a quasi-zero stiffness (QZS) vibration isolator with double-arc flexible beams (D-AFB) is proposed. The QZS isolator consists of D-AFB units, the base, platform, fixture, guide rail, and linear bearing. The static performance of D-AFB is analyzed using the FEA method, and the QZS condition is obtained. The harmonic balance method (HBM) and the pseudo arc length method (PALM) are used to solve the dynamic equations of the nonlinear system, and the analytical solutions of displacement transmissibility and Force transmissibility are derived. In theory, the initial frequency is 77.6 % lower than that of the equivalent linear system. The QZS characteristic of D-AFB is verified by static experiment, and the low-frequency isolation performance of the QZS isolator is verified by dynamic experiment under constant amplitude and constant acceleration excitation. The D-AFB has a simple structure and can easily satisfy QZS conditions. So the D-AFB can be customized according to load requirements. Multiple vibration isolation loads can be obtained by adjusting the assembly of the D-AFB. The QZS isolator can adapt to load changes within 10 % and has an isolation effect on vibrations above 4 Hz. The idea of designing a QZS isolator with D-AFB as an array unit has a good research prospect and great application value in meeting the requirements of miniaturization and integration.

Origami-inspire quasi-zero stiffness structure for flexible low-frequency vibration isolation

As an emerging technology, origami exhibits rich nonlinear static and dynamic properties. However, simulating creases remains a key challenge hindering practice application, especially for volumetric (deformable) origami. Inspired by the bistable behavior and axial-rotational coupling mechanism of triangulated cylindrical origami (TCO), this paper proposes a novel combined truss-spring structure with additional inertial mechanism (TCTS-RIM) for low-frequency vibration isolation. Unlike pure TCO, the TCTS-RIM uses elastic linkages to simulate all creases and modifies crease positions, enhancing physical realization in engineering applications and offering tunable stiffness and inertia on demand. Static analysis shows the modified truss-spring structure in TCTS-RIM has superior quasi-linear negative stiffness compared to pure TCO, which enables a very wide quasi-zero stiffness (QZS) range via linear spring compensation. The wide QZS range for different loads can be realized by setting appropriate structural parameters. From system dynamic equations, nonlinear inertia, nonlinear quadratic force, and nonlinear damping due to RIM are identified and discussed. The Alternating frequency–time harmonic balance method is used to obtain the displacement transmissibility, and its parametric influencing investigations verify that the proposed TCTS-RIM has excellent low-frequency vibration isolation performance and rich tunability. Comparative discussions show the wide QZS range significantly reduces the resonance frequency, broadens the isolation frequency band, and yields superior dynamic performance versus pure TCO isolators. Moreover, equivalent mass, anti-resonance and softening behavior induced by the rotational inertia mechanism further enhance low-frequency vibration isolation performance. An experimental prototype is built, and experimental results validate the correctness of the theoretical analyses. This work presents a simple mechanical implementation of volumetric origami, which may progress the engineering applications of origami and provide a viable approach to low-frequency vibration control.

A3-DOF frog-inspired quasi-zero stiffness isolator and its vibration control performance

To pursue a nonlinear isolator with simpler structure, better load adaptability, and wider quasi-zero stiffness (QZS) region, a 3-DOF bionic vibration isolation device is proposed and analyzed inspired by the superior landing performance of the frog's leg structure. The mechanism's dynamical equation is established using Lagrange's principle. The dynamic model is validated using ADAMS simulation. The effects of spring stiffness and rod length on static mechanical characteristics are analyzed. The vibration attenuation performance of the structure is analyzed under independent three-directional excitation and three-directional coupled excitation. Compared with the typical X-shaped QZS isolator and the traditional QZS isolator, the designed structure's advantages is demonstrated. By tuning the parameters and building a control route based on variable-stiffness dielectric elastomer, optimization of the device's vibration isolation performance under coupled excitation was accomplished.

Wide quasi-zero stiffness region isolator with decoupled high static and low dynamic stiffness

Quasi-zero stiffness (QZS) isolators can achieve the two goals of relatively high static and low dynamic stiffness (HSLDS). However, the static and dynamic stiffness of most QZS isolators remains coupled, causing conflicts in optimizing these dual objectives, especially in the case of large displacement excitations and heavy loads, leading to limited performance. To overcome these limitations, this paper presents an isolator with an extended QZS region that allows for the independent design of HSLDS. The positive stiffness provided by the cantilever beam with curve fixture (CBCF) precisely counteracts the negative stiffness offered by a pair of inclined springs, thereby achieving continuous and extensive QZS characteristics from a point to a region. Dynamic equations are established based on the Lagrangian principle and swiftly solved utilizing the Runge-Kutta-4 method. The proposed isolator exhibits a low resonance frequency, and superior performance when exposed to large displacement excitations compared to alternative isolators. Both static and dynamic experiments confirm a QZS region of 0.023 m and resonance frequencies of below 1 Hz. The proposed isolator facilitates effective vibration isolation for ultra-low-frequency and large displacement excitations.

Gas-Spring Quasi-Zero Stiffness Air Damping Isolator for Vertical Vibration Control of Indoor Substation Excited by Metro Loads

To mitigate the metro-induced vertical vibration of the indoor substation structure, this study proposes a gas-spring quasi-zero stiffness air damping isolator (AD-QZSI) with excellent low dynamic stiffness and high-static stiffness characteristics. The working principle and mechanical properties of the AD-QZSI are introduced and studied through theoretical and numerical methods. A model for substation considering soil–structure–equipment interaction is established using the software ABAQUS, its accuracy is validated based on a series of measured data from actual projects, and the AD-QZSI’s simulation method and parameter design method are described in detail. The air damper’s stiffness [Formula: see text] is integrated into the isolator’s mechanical model, theoretically and numerically achieving an accurate simulation of AD-QZSI’s nonlinear mechanical properties. The numerical results have an error of less than 5% with the measured data, indicating that the model is able to better capture the actual structure’s dynamic characteristics and is reasonable to be employed for subsequent analysis. Numerical results show that AD-QZSI can significantly reduce the structural vertical vibration, and its control effect is better in the whole frequency band, in particular, the effect is also visible in the low-frequency band, indicating that its vibration isolation frequency band is wider than that of traditional QZS isolator. With the vibration source distance increasing, the control effect of AD-QZSI presents a tendency to decrease and then level off, and its vibration isolation gain is weakened by the continuous increase of the damping ratio greater than 0.01. Moreover, the equipment’s dynamic amplification factor of the isolated structure decreases significantly. Finally, the proposed AD-QZSI can obtain ideal quasi-zero stiffness characteristics by adjusting the air pressure, and the adopted air damper belongs to the green low-carbon components, featuring great practical value and application prospects.

Design and test of a quasi-zero stiffness isolator with machinable springs

Quasi-zero stiffness (QZS) vibration isolators are widely used for vibration isolation due to their high performance, but their low load-carrying capacity limits their applications. In this paper, a heavy-load-bearing QZS vibration isolator consisting of three compression springs is investigated for isolating ultra-low frequency vibrations. From the theoretical aspect, parameter optimization considering both load mass and isolation performance metric (IPM) is implemented, and a parameter guidance diagram is proposed for parameter design. From the practical point of view, two innovative springs are designed and fabricated by wire-electrical discharge machining (W-EDM), referring to the idea of compliant mechanism. These creative designs are endowed with precise stiffness, large compression and buckling avoidance, which further improve the system properties. Finally, a prototype is made and experiments are carried out to verify the effectiveness of the design. Compared with linear isolators, the experimental results of QZS isolator show better isolation performances in a wider frequency range.

A generic design motif for metamaterials with controllable nonlinearity & guided deformation

Structure design motifs take an essential role in creating materials or metamaterials with superior mechanics or special functions. However, a fundamental question naturally arising and remaining unknown is related to how to effectively design an engineered material structure with “adjustable and predictable” nonlinear mechanic properties conveniently. Here we propose a very simple but versatile design motif, named as bq-structure, which can provide superior flexibility in achieving various nonlinear properties, including 200 % larger and designable ranges of quasi-zero stiffness, negative stiffness, and multi-stable stiffness, etc, that original material or traditional beam-based design motifs cannot provide. The proposed design motif has sufficient reliability in nonlinear manipulation with a “guided & controllable” manner instead of “trail-and-error attempts” existing in most existing ones. A prototyped vibration isolation unit can achieve a resonant frequency less than 1 Hz easily which cannot be done with many other methods of similar size and payload. Given the large elastic deforming capacity and ductility in structural scale, the superb nonlinearity regime is generally designable with various structure parameters, uniquely providing a superior optimization tool with this novel design motif considering various real application requirements for advanced materials design, energy storage or conversion, mechanical vibration mitigation, and robotic systems etc.

Resonance response and chaotic analysis for an irrational pendulum system

We propose a novel rotating pendulum system with irrational nonlinearity, bi-stable phenomenon and quasi-zero stiffness characteristic, which bears a transition from standard double well dynamics to discontinuous double well dynamics by adjusting a geometric parameter. Nonlinear dynamical behaviors of the proposed irrational pendulum system subjected to viscus damping and periodic excitation are studied. To analytically demonstrate the primary resonance response for this perturbed irrational pendulum system, we introduce an approximate irrational system which is significant parallels with the original pendulum system from the perspective of qualitative analysis and quantitative calculation. Averaging method is applied to investigate the dynamic response of the perturbed irrational pendulum system with quasi-zero stiffness at origin. The effect of the internal and external parameters on the response curves are discussed. Numerical fitting technique and semi-analytical Melnikov method are used to detect the chaotic boundaries of the perturbed irrational pendulum system with two types of homoclinic orbits. Different types of periodic solutions and chaos are clarified in the perturbed irrational pendulum system by using numerical simulations. It is found that a class of chaos with oscillatory and rotational motions bears significant similarities to paroxysmal chaos due to sudden rotational motion and two chaotic motions formed by period-doubling bifurcation merge into one chaos.