Quasi-zero Stiffness Vibration Research Articles

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.

Bio-inspired quasi-zero stiffness vibration isolator with quasilinear negative stiffness in full stroke

Simpler structure, better adaptability to variable loads, and wider linear stable region have always been pursued by nonlinear quasi zero stiffness (QZS) isolator. Inspired by the balancing and stabilizing effect of the leg and wing in the take-off and landing of birds, this paper proposes a novel bio-inspired QZS vibration isolator (BI-QZSVI). The BI-QZSVI is composed of two primary components: the legged negative stiffness structure, which comprises a two-link mechanism and a set of oblique springs, and a pair of vertical springs that imitate wings. A static model is established based on the virtual work principle, the nonlinear dynamic model is then constructed using Lagrangian equations, and an analytical solution is derived through implementation of the harmonic balance method. An experimental platform is established to verify the effectiveness of the theoretical results. The results reveal that the proposed isolator outperforms existing typical isolators by offering a larger quasi-zero stiffness region, as evidenced by the two proposed range and linearity indexes. The unique structure effectively tackles geometric nonlinearity to establish a linear relationship between the load and stiffness. Notably, the negative stiffness of the isolator exhibits exceptional linearity throughout the entire stroke, ensuring a broad stability region even under high excitation levels. Furthermore, the isolator demonstrates remarkable efficacy in reducing vibrations with frequencies exceeding 3 Hz. Overall, the proposed isolator is an efficient low-frequency isolator with simple structure, strong adaptability, and wide linear range.

Active Control of Quasi-Zero-Stiffness Vibration Isolator with Variable Load

Quasi-zero-stiffness (QZS) isolator has great application potential in the field of low-frequency vibration isolation due to its high-static and low-dynamic (HSLD) nonlinear stiffness characteristic, but it is precisely this characteristic that makes it very sensitive to load changes. Once the load changes, causing it to deviate from the equilibrium position, it no longer qualifies zero-stiffness characteristic, and the vibration isolation capacity will be significantly decrease. To make the QZS isolator possess variable load capacity and be more suitable for engineering practice, an active QZS vibration isolator based on electromagnetic actuator is designed in this paper, which eliminates the influence of load changes through the active force of the electromagnetic actuator. First, the dynamic equation of the isolator is established by Newton–Euler method, and the dynamic characteristic of the isolator under standard load and load variations are analyzed through improved incremental harmonic balance (IHB) method based on discrete Fourier transform (DFT). Next, the improved particle swarm optimization (PSO) algorithm are employed to optimize the Proportion Integration Differentiation (PID) controller parameters. Then, the vibration isolation performance of QZS isolator in controlled and uncontrolled and linear systems in the same control state are compared in frequency domain and time domain, respectively. Finally, the performance of active QZS isolator under load variation is discussed. The results indicate that the isolation performance of the QZS isolator under active control is significantly better than in uncontrolled conditions and the controlled linear system. When the load changes, real-time compensation through the actuator output control force can also enable the QZS isolator to achieve a better vibration isolation performance.

Theoretical and experimental study of a novel nonlinear quasi-zero Stiffness vibration isolator based on a symmetric link-rod-type structure

This study proposes a novel nonlinear low-frequency vibration isolator with quasi-zero stiffness (QZS) based on a symmetric link-rod-type structure. The principle of the isolator is analyzed, and the properties of the vibration isolator are investigated experimentally. Varying displacements with a restoring force and stiffness are acquired by a static model; thus, the QZS conditions and system contributing factors are elucidated. Various effects of the excitation amplitude, damping ratio, rod length ratio, and initial spring compression ratio on the displacement transmissibility, which are determined using the harmonic balance method (HBM), are discussed. Through a series of experiments on the isolator prototype, the performance of a QZS vibration-isolation system with a symmetric link-rod-type structure is validated. The results indicate that the presented symmetric link-rod-type QZS vibration isolator has a wider QZS interval, lower frequency of vibration isolation, and better isolation performance, providing a valuable reference for the design of QZS vibration isolators.

Bio-inspired multi-joint-collaborative vibration isolation

Inspired by the collaborative action of ankle, knee and hip joint, a novel bio-inspired multi joint structure (BIMJS) is proposed, and its favorable nonlinearity is systematically investigated for low frequency vibration isolation. Two rigid rods are adopted to imitate the femur and tibia, and three torsional springs are utilized to simulate the muscle function in each joint. Based on the principle of virtual work, a static model considering the action of three joints and leg posture is established to characterize the stiffness property. The independent action mechanism of each joint is revealed and the influence of posture adjustment on equivalent stiffness of the BIMJS is studied. By adjusting proper posture and setting reasonable stiffness of each joint, the quasi zero stiffness (QZS) can be easily obtained for low frequency vibration isolation. Dynamic model is developed and the displacement transmissibility is derived to estimate the isolation performance of the BIMJS. The experimental results confirm the advantages of realizing QZS and low-frequency vibration isolation under multiple loads. The vibrations above 2.5 Hz can be effectively isolated. The concept of utilizing the collaborative action of multi joints may provide an innovative method for the design of low frequency vibration isolators.

Load-adaptive quasi-zero stiffness vibration isolation via dual electromagnetic stiffness regulation

Conventional quasi-zero stiffness (QZS) isolators are sensitive to load variation, especially the load mismatch can severely degrade low-frequency vibration isolation performance. Herein, a load-adaptative electromagnetic QZS vibration isolator (LEQVI) is proposed. The stiffness nonlinearization for QZS characteristic is achieved by exploiting a nonlinear positive stiffness structure (a cylindrical coil and a magnet in the face-to-face configuration) to modulate a negative stiffness structure (a conical coil and a magnet in the nested configuration). Static modeling and tests reveal that the rated load of the LEQVI can be flexibly and linearly adjusted by regulating the excitation current. Dynamic modeling found that the load mismatch can narrow the vibration isolation bandwidth and deteriorate the vibration attenuation effect. A sliding mode control law considering input saturation is developed to adapt to unknown loads. Simulations and dynamic experiments are conducted to evaluate the vibration isolation performance and verify the effectiveness of the load-adaptive controller. The results demonstrate that the LEQVI can realize a wide vibration isolation band and effective vibration attenuation under various loads via dual electromagnetic stiffness regulation. The proposed LEQVI provides a novel perspective for designing load-insensitive QZS isolators and holds great promise in facilitating future engineering applications of QZS isolators.

Further investigation and experimental study of an origami structure-based quasi-zero-stiffness vibration isolator

A quasi-zero stiffness (QZS) vibration isolator formed from a truss-spring stacked Miura-ori (TS-SMO) origami structure can provide a desired ultra-low dynamic stiffness for vibration isolation while remaining a high-static stiffness for load supporting capacity. This paper further investigates the design parameters and experimentally studies the dynamic performance of the proposed TS-SMO vibration isolation system. The effects of the spring parameters and the initial setup conditions on its static response are analysed. With the proper parameter selection, the resultant supporting force generated by the origami structure can be expressed as a polynomial containing the static force and dynamic force components which does not have the linear term. The displacement transmissibility of the proposed system is calculated to evaluate its isolation performance. Analytical and numerical results are in good agreement and both demonstrate an ultra-low resonance frequency for vibration isolation. The dynamic behaviour of the proposed system is also investigated under different conditions to enhance the vibration isolation performance. A proof-of-concept prototype is designed, fabricated and tested to verify both static and dynamic performances of the TS-SMO QZS isolator. The comparative experimental results between the corresponding linear isolation system and the proposed nonlinear QZS system validate the design of origami-inspired structure for vibration isolation and further confirm the effectiveness of the QZS vibration isolator. It is hoped that this research would provide a solid foundation for designing and modelling the TS-SMO structure adopted for vibration isolation in practical engineering applications.

A new magnetorheological quasi-zero stiffness vibration isolation system with large zero stiffness range and highly stable characteristics

Various quasi-zero stiffness (QZS) systems have been developed and applied in the vibration control domain in recent years. However, most QZS systems are usually unstable against external disturbances, and their QZS ranges are very limited. To address these issues, this study develops a highly stable QZS vibration isolation system integrated with magnetorheological fluids (MRFs). The MRFs endow the vibration isolation system with stiffness variability in vertical and lateral directions to against external disturbances, which innovatively solves the unstable problem of QZS systems. Meanwhile, the stiffness variability also makes the system adaptable to vibrations with different frequencies, so the system can deliver the best vibration isolation performance in response to various excitations. The system consists of a vertical isolation unit and a lateral isolation unit. By paralleling a nonlinear positive stiffness QZS component with a nonlinear negative stiffness QZS component in the vertical isolation unit, a large QZS range in the vertical direction and smaller stiffness are realised, thus improving the vibration isolation performance. In this study, the vibration isolation system is designed and prototyped; its QZS characteristics and adjustable stiffness features in both the vertical and lateral directions are experimentally verified; the frequency responses of the system are obtained experimentally; and the stability and the vibration isolation performance of the system are also evaluated by experiments with the designed control algorithms. This study provides a solution to overcome the unstable problem of QZS systems and extend the limited QZS range, whilst realising QZS characteristics in both vertical and lateral directions, thus broadening the application of QZS systems.

Theoretical modeling and analysis of a quasi-zero-stiffness vibration isolator equipped with extensible and axially magnetized negative stiffness modules

Quasi-zero-stiffness (QZS) isolation systems have demonstrated good performance in low-frequency vibration isolation fields. However, the existing QZS isolation systems with traditional negative stiffness elements cannot support high payloads under miniaturization and simplification. To give some beneficial insights into high loading capacity, optimized structure, and good vibration isolation performance, a novel axially magnetized negative stiffness module (MNSM) is proposed based on the concepts of modularity and expansibility. Concretely, an axially magnetized negative stiffness unit (MNSU) is designed as the fundamental building block of MNSM, and the proposed MNSM can be composed of different axially magnetized negative stiffness units (MNSUs) for diversified requirements. To effectively investigate the characteristics of the MNSU, a computationally high efficient equivalent surface current method is developed. As a result, two types of MNSUs with optimized parameters are achieved, and their design procedures are presented respectively. To verify the benefits of the MNSMs, the designed QZS isolator is theoretically modeled and solved with the average method and then verified through the Runge–Kutta method. Through analyzing the isolation systems with MNSMs under different nonlinearities and dynamic parameters, the results indicate that the proposed MNSMs can endow the QZS vibration isolator with a lower resonant frequency, a wider isolation frequency range, and a smaller transmissibility. Additionally, it is also demonstrated that there is an inverse relationship between the complexity of the MNSM structure and the sensitivity of the isolation system.

Analytical modeling of a device for vibration isolation and energy harvesting using simply-supported bi-stable hybrid symmetric laminate

The bi-stable hybrid symmetric laminate (BHSL) has been investigated for vibration isolation and energy harvesting, by taking advantage of its bi-stable characteristic. A device using simply-supported BHSL is proposed to integrate these two functions. This device is called the quasi-zero-stiffness (QZS) vibration isolator with a piezoelectric element (PE). An equivalent theoretical model is developed based on the restoring force-displacement curve of BHSL. The approximate analytical solutions and direct numerical solutions are obtained by the harmonic balance method and the Runge-Kutta method, respectively. Displacement transmissibility is utilized to quantify the vibration isolation performance of this vibration isolator. The influences of the excitation amplitude, the length of BHSL, the width of BHSL and the load resistance are analyzed. The results show that adjusting these parameters can improve the vibration isolation performance and energy harvesting performance. The QZS vibration isolator with PE achieves the goal of higher power density under a low-frequency and low-amplitude excitation and simultaneously has a good vibration isolation performance.

Design and Development of Structural Parameter Identification Software for Nonlinear Vibration Isolators

This paper developed an object-oriented software to facilitate parameter calibration of the quasi-zero stiffness (QZS) vibration isolator for engineering applications. Considering its advantages of convenient programming and high noise resistance, we employ the harmonic balance method to construct the identification core algorithm. The developed software consists of data pre-processing, parameter identification, and post-processing modules. The data pre-processing module imports and classifies all the required data. Then, the parameter identification module conducts preliminary nonlinearity analysis so that nonlinear structural parameter identification can be successfully carried out. After parameter identification, the data post-processing module displays and stores the identified results. The performance of the software is tested by a numerical example of a two-degree-of-freedom QZS vibration isolator, proving the software can give accurate identification results within a few user-friendly graphical interfaces. Based on this software, we hope that the application and promotion of nonlinear system parameter identification become more convenient.

Quasi-Zero Stiffness-Based Synchronous Vibration Isolation and Energy Harvesting: A Comprehensive Review

In recent years, the advantages of nonlinearity in vibration isolation and energy harvesting have become increasingly apparent. The quasi-zero stiffness (QZS) of the nonlinear term provided by the negative stiffness element can achieve vibration isolation under low-frequency environments while improving the efficiency of energy harvesting. The QZS provides a new research idea for simultaneous vibration isolation and energy harvesting. The main purpose of this paper is to review past research results, summarize possible problems, and discuss trends. After briefly analyzing the basic principle of QZS vibration isolation, the progress of QZS in vibration isolation and energy harvesting in recent years is reviewed. At the same time, main challenges of QZS in realizing synchronous vibration isolation and energy harvesting are also discussed. Finally, according to the existing QZS challenges, the future development trend of QZS is proposed. This paper would provide a quick guide for future newcomers to this field.

Recent Advances in Quasi-Zero Stiffness Vibration Isolation Systems: An Overview and Future Possibilities

In recent decades, quasi-zero stiffness (QZS) vibration isolation systems with nonlinear characteristics have aroused widespread attention and strong research interest due to their enormous potential in low-frequency vibration isolation. This work comprehensively reviews recent research on QZS vibration isolators with a focus on the principle, structural design, and vibration isolation performance of various types of QZS vibration isolators. The negative-stiffness mechanism falls into two categories by different realization methods: passive and active/semi-active negative-stiffness mechanisms. Representative design, performance analysis, and practical application are elaborated for each category. The results show that passive vibration isolation systems have excellent low-frequency vibration isolation performance under specific payload and design parameters, whereas active/semi-active vibration isolation systems can better adapt to different environmental conditions. Finally, the development trends and challenges of QZS vibration isolators are summarized, and the solved and unsolved problems are highlighted. This review aims to give a comprehensive understanding of the QZS vibration isolation mechanism. It also provides guidance on designing new QZS vibration isolators for improving their vibration isolation performance and engineering applicability.

A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms

Vibration isolation is one of the most efficient approaches to protecting host structures from harmful vibrations, especially in aerospace, mechanical, and architectural engineering, etc. Traditional linear vibration isolation is hard to meet the requirements of the loading capacity and isolation band simultaneously, which limits further engineering application, especially in the low-frequency range. In recent twenty years, the nonlinear vibration isolation technology has been widely investigated to broaden the vibration isolation band by exploiting beneficial nonlinearities. One of the most widely studied objects is the “three-spring” configured quasi-zero-stiffness (QZS) vibration isolator, which can realize the negative stiffness and high-static-low-dynamic stiffness (HSLDS) characteristics. The nonlinear vibration isolation with QZS can overcome the drawbacks of the linear one to achieve a better broadband vibration isolation performance. Due to the characteristics of fast response, strong stroke, nonlinearities, easy control, and low-cost, the nonlinear vibration with electromagnetic mechanisms has attracted attention. In this review, we focus on the basic theory, design methodology, nonlinear damping mechanism, and active control of electromagnetic QZS vibration isolators. Furthermore, we provide perspectives for further studies with electromagnetic devices to realize high-efficiency vibration isolation.

A non-smooth quasi-zero-stiffness isolator with displacement constraints

Quasi-zero-stiffness (QZS) mechanism is one of the significant solutions with its distinct advantage to the low-frequency vibration isolation problems in mechanical vibration. However, subject to the limitation of its effective range of very narrow, the strong nonlinearity of the single QZS mechanism under large-amplitude excitation might induce an undesirable large-amplitude vibration or even damage some essential equipment. Therefore, this paper designs a double-layer QZS vibration isolator with displacement constraints to reduce the undesirable large-amplitude vibration. Firstly, the mechanical model of a double-layer QZS vibration isolator with displacement stops is established based on Hertz's contact model (DLQZS-HCM). Subsequently, the incremental harmonic balance method is employed to examine the vibration isolation performance theoretically. The system parameters are then analyzed to explore their influences on the isolation performance. Compared with the double-layer linear isolator (DLL) and double-layer QZS isolator (DLQZS), it is found that the DLQZS-HCM isolator can perform better in both extending the frequency range of vibration isolation and decreasing the peak transmissibility when undergoing large-amplitude excitation. Finally, in order to further enhance the isolation performance at low-frequency levels, feedback control is applied to the DLQZS-HCM isolator. The obtained results reveal that the increasing displacement feedback gain can significantly broaden the vibration-isolation range of the DLQZS-HCM isolator in the frequency area tending to zero.

Energy Transfer of an Axially Loaded Beam With a Parallel-Coupled Nonlinear Vibration Isolator

Abstract Traditional vibration isolation of satellite instruments has an inherent limitation that low-frequency vibration suppression leads to structural instability. This paper explores a parallel-coupled quasi-zero stiffness (QZS) vibration isolator for an axially loaded beam, with the goal of enhancing the effectiveness of low-frequency isolation. A QZS contains two magnetic rings, which contribute negative stiffness, and one spiral spring, with positive stiffness, a combination that has high static stiffness to resolve the structural instability. The frequency response functions (FRFs) of power flow are used to measure the effectiveness of vibration isolation. The magnetic stiffness of the magnetic rings is calculated using the principle of equivalent magnetic charge. The heights, radii, and gap of the magnetic rings affect its stiffness. The parallel-coupled QZS vibration isolator of an axially loaded beam is modeled using an energy method. Based on the Galerkin truncation, harmonic balance analysis, and arc-length continuation, an approach is proposed to analyze the FRFs of power flow for the parallel-coupled QZS vibration isolation of an axially loaded beam. Numerical results support the analytical results. Both analytical and numerical results show that the power reduction of axially loaded beams with a parallel-coupled quasi-zero vibration isolation system is more significantly suppressed at low frequencies.

A nonlinear quasi-zero-stiffness vibration isolation system with additional X-shaped structure: Theory and experiment

A novel nonlinear quasi-zero-stiffness (QZS) vibration isolation system with high load carrying capacity is proposed. By connecting X-shaped structure with a platform, the quasi-zero-stiffness vibration isolation system with additional X-shaped structure (X-QZS) is designed. The relationships of system restoring force and stiffness related to displacement are obtained by static modelling, and the influences of the parameters on the system stiffness are analyzed. In the dynamic analysis, the amplitude-frequency characteristics and transmissibility curves are calculated by the harmonic balance method. The correctness of the calculation results is verified by numerical simulation and vibration experiments. From the investigations, it is observed that the designed X-QZS system has a wide QZS interval, a small unstable interval, a low jump-down frequency, and a high load carrying capacity. These results can provide a useful reference for improving the performance of QZS vibration isolation systems.

A quasi-zero-stiffness isolator with a shear-thinning viscous damper

Quasi-zero-stiffness (QZS) vibration isolators have been widely studied, because they show excellent high static and low dynamic stiffnesses and can effectively solve low-frequency and ultralow-frequency vibration. However, traditional QZS (T-QZS) vibration isolators usually adopt linear damping, owing to which achieving good isolation performance at both low and high frequencies is difficult. T-QZS isolators exhibit hardening stiffness characteristics, and their vibration isolation performance is even worse than that of linear vibration isolators under a large excitation amplitude. Therefore, this study proposes a QZS isolator with a shear-thinning viscous damper (SVD) to improve the vibration isolation performance of the T-QZS isolators. The force-velocity relation of the SVD is obtained, and a dynamic model is established for the isolator. The dynamic responses of the system are solved using the harmonic balance method (HBM) and the Runge-Kutta method. The vibration isolation performance of the system is evaluated using force transmissibility, and the isolator parameters are analyzed. The results show that compared with the T-QZS isolators, the proposed QZS-SVD isolator achieves the lower initial vibration isolation frequency and peak value, and exhibits better vibration isolation performance at medium and high frequencies. Moreover, the proposed isolator can withstand a large excitation amplitude in the effective vibration isolation range.

The effect of various damping on the isolation performance of quasi-zero-stiffness system

A quasi-zero-stiffness (QZS) vibration isolation system was designed to attenuate low-frequency and ultra-low-frequency vibrations. Because nonlinearity exists in QZS systems, various nonlinear dynamic behaviours inevitably influence the vibration isolation performance. Thus, damping is the key for suppressing nonlinear effects. The effects of three types of damping, viscous damping, hysteretic damping, and nonlinear hysteretic damping on the QZS vibration isolator are discussed in this paper. The Duffing-Ueda equation was used to describe the dynamic motion of the QZS system, which was solved using the harmonic balance method (HBM). Two hybrid-damping models were then proposed to avoid unbounded nonlinear responses for excessive base excitation. Based on theoretical and numerical analysis, the effect of the two hybrid damping models, the hysteretic-nonlinear hysteretic (H-NH) damping model and viscous-hysteretic-nonlinear hysteretic (V-H-NH) damping model, on the transmissibility is discussed in detail. To verify the theoretical results, QZS isolator prototypes with two types of hybrid damping were designed and manufactured. A hydraulic damper and a thermoplastic rubber (TPR) damper were used respectively in the two models of the experiments. The experimental results reveal that the isolator with hybrid linear and nonlinear damping provides a better isolation effect for both low-and high-frequency vibrations.

Lever-type quasi-zero stiffness vibration isolator with magnetic spring

Unlike the tuning of the vibration isolation band through stiffness and geometric parameters in traditional quasi-zero stiffness (QZS) vibration isolators (VIs), this study presents a lever-type QZS vibration isolator (L-QZS-VI) to improve the vibration isolation performance. The QZS characteristic is realized with a magnetic spring. Eddy current damping (ECD) is used to eliminate the jump phenomenon and improve the vibration isolation performance. A theoretical model of L-QZS-VI with ECD is developed and the corresponding governing equation is obtained using the Lagrange equation. The displacement transmissibility is derived using the harmonic balance method. The effects of the tip mass of the lever, lever ratio, nonlinear stiffness of the magnetic spring and excitation amplitude on the vibration isolation performance of the L-QZS-VI are analyzed numerically and experimentally. The vibration isolation performance can be largely improved by tuning the lever ratio, tip mass of the lever, and nonlinear stiffness of the magnetic spring. The ECD can produce tunable damping to further improve the vibration suppression performance in the resonance region. This study provides a guideline to design, model, and optimize L-QZS-VI.