Quasi-zero Stiffness Isolator Research Articles

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.

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.

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.

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.

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.

Bifurcation and dynamic analysis of quasi-zero stiffness isolator with asymmetric stiffness and mismatched load based on X-shaped negative stiffness structure

Bifurcation and dynamic analysis of quasi-zero stiffness isolator with asymmetric stiffness and mismatched load based on X-shaped negative stiffness structure

Investigation on the free vibration characteristics of vertical quasi-zero stiffness isolation system considering the disc spring's loading position

This study investigates a quasi-zero stiffness (QZS) isolation system designed for vertical vibration control in isolation structures. The QZS characteristics are achieved by connecting a negative stiffness disc spring in parallel with the linear positive stiffness spiral spring. Initially, the force-displacement relationship of the disc spring is established, taking into account the loading position, and validated through static experiments. Subsequently, the free vibration equations of the QZS system are derived. The Jacobi elliptic functions and the Newton-harmonic balance (NHB) method are then employed to study its free vibration characteristics without considering damping. The results demonstrate that the natural vibration period of the QZS system is related to the nondimensional amplitude and the height of the loaded inner cone. Furthermore, the second-order analytical approximate solution obtained via the NHB method exhibits remarkable accuracy. Finally, the critical damping ratio of the damped QZS isolation system is investigated using a numerical approach. The findings indicate that the critical damping ratio is only correlated with the nondimensional amplitude. This study addresses the gaps in existing research and provide recommendations for the parametric design of vertical QZS isolation system.

Research on flexible beam-type nonlinear vibration isolators suitable for low frequencies

Ship vibration not only causes safety issues, but also easily generates noise pollution. Therefore, this paper introduces the quasi-zero stiffness (QZS) vibration isolator to solve the problem of low-frequency vibration. In terms of static analysis, this paper proposes a discretized beam constraint model (DBCM) to study the static properties of flexible beams with large deformation, and the finite element analysis (FEA) verifies the accuracy of DBCM. Regarding dynamic analysis, this paper combines the harmonic balance method (HBM) and the pseudo-arc length method (PALM) to analyze the dynamic response and explore the influence of excitation and damping ratio on the response stability. In addition, the performance of equivalent linear isolators is compared, revealing significant advantages of QZS isolator in terms of isolation bandwidth and peak transmissibility. The experimental data demonstrates that QZS isolator’s initial isolation frequency (2.14 Hz) is 68.5% lower than that of linear isolators (6.79 Hz), and the isolation efficiency at 5.35 Hz can reach 90%, making it suitable for low-frequency isolation. Furthermore, experimental data validate the accuracy of the theoretical model and FEA. The static and dynamic theoretical models can optimize the structural parameters of flexible beams and serve as valuable inspiration and reference for designing and improving isolator.

A novel permanent magnet vibration isolator with wide stiffness range and high bearing capacity

Quasi-zero stiffness (QZS) vibration isolators have attracted extensive attention because of their excellent performance in low-frequency vibration isolation and high bearing capacity. However, its practical engineering application remains challenges due to the magnitude and adaptability of the negative stiffness. This paper proposes a permanent magnet type variable stiffness (PMVS) mechanism with a wide stiffness range from negative to positive. Based on the semi-analytical model of magnetic force, the QZS isolator composed of the spiral spring in parallel with the PMVS mechanism is developed, which has both stiffness adjustment and load adaptability. The nonlinear dynamic equation with 5th polynomial restoring force is established then solved by the harmonic balance method (HBM). The dynamic behaviours is investigated and validated through the experimental prototype and good isolation performance is observed. Building upon the wide stiffness adjustment and large magnitude of the PMVS mechanism. the proposed isolator achieves a stiffness range of 4.15–153.45 N/mm under a safe load up to 120 kg, which implies that the natural frequency of the isolator can reach an ultralow value of 0.93 Hz within the safe load (120 kg).

Study on vibration response and isolation of substation structure under subway load excitation

This study takes the indoor substation adjacent to the elevated bridge subway line as the engineering background, investigates the structural vibration response law of the substation induced by the operation of the subway line through on-site vibration measurement, and proposes a novel nonlinear gas-spring quasi-zero stiffness isolator (NGS-QZSI) is proposed to reduce the structural vertical vibration and further reduce the safety distance. The software ABAQUS is used to establish a structure-equipment coupling numerical analysis model considering soil-structure interaction, and its effectiveness and accuracy are validated based on the measured results. The structural vibration response analysis is carried out under different vibration source distances, and a nonlinear gas-spring quasi-zero stiffness isolator is proposed to be employed for substation structural vibration isolation. The research results show that the substation structure under subway load excitation is dominated by vertical vibration, and its vibration response increases gradually with the increase of floor level. When the substation structure is less than 45 m from the subway line, the structural response exceeds the safety limit (12.5 μm/s) of the VC-C standard. With the vibration isolator attached, the structural vibration response is significantly reduced, with the peak and root mean square response controlled by more than 70 %. Particularly, the safe distance of the substation from the subway line is reduced from 45 m to 20 m. Moreover, the frequency domain result analysis indicates that the proposed nonlinear vibration isolator can effectively control the low-frequency vibration of the structure.

Review of Lightweight Vibration Isolation Technologies for Marine Power Devices

Vibration induced by marine power devices (MPD) transmitting to the hull structure is one of the most important factors that cause ship vibration and underwater sound radiation. Vibration isolation technologies (VIT) are widely applied to reduce the vibration transmission. However, the overweight issue of VIT for marine power devices is a currently challenging engineering problem. The current reserve of lightweight and high-efficiency VIT for MPD and relevant theoretical and design research are seriously insufficient. This article first elaborates the causes of the overweight problem of VIT for MPD: (1) failing to grasp the quantitative law; (2) single vibration suppression mechanism. Then, it systematically sorts out the technical methods and application examples with potential to solve the overweight problem, such as dynamic optimization design, lightweight material method, novel intermediate mass structures, distributed dynamic vibration absorbers (DDVAs), locally resonant structures (LRS), particle damping (PD), quasizero stiffness isolators (QZSI), and active vibration control (AVC) technologies. Finally, the future development of lightweight VIT for MPD is prospected. It can be used as a reference for marine vessel vibration attenuation research and engineering design.

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.

Study on the performance of a novel 1DOF isolator with QZS characteristics

A typical one-degree-of-freedom (1DOF) shock isolator that has quasi-zero stiffness (QZS) characteristics consists of two transversal springs and one portrait spring. The transversal springs can provide negative stiffness and the vertical spring is used as a load-bearing component. In this article, an improved 1DOF QZS shock isolator is obtained by utilizing the combination of lateral bars and springs. The displacement transmissibility under the harmonic excitation is obtained and the principle of minimum displacement transmissibility under the condition of system stability is proposed. Finally, numerical simulation is conducted, and the simulation results reflect that the proposed 1DOF QZS isolator significantly performs better than the previous one.

Local gravity control method for solving load-mismatch issue in isolators

Quasi-zero stiffness (QZS) shows significant advantages in low frequency vibration isolation. However, the isolation performance is heavily dependent on the rated load and prone to load-mismatch. Here, a general local gravity control method (LGCM) is proposed to eliminate these limitations by introducing an expected constant force to adjust the equivalent gravity of the mismatched load. As a result, the isolators can be maintained at an ideal static equilibrium point with low dynamic stiffness. The load-mismatch was investigated and emphasized combined with the spring-link mechanism (SLM). The analysis indicated that the load-mismatch results in stiffness hardening, natural frequency increasing, and vibration isolation band shortening. The principle of the LGCM was fully revealed in the respect of conceptual design, electromechanical coupling analysis, control system and operation mechanism. The harmonic balance method (HBM) was used to model the response of the periodic and sweep excitation. The electromechanical coupling simulation was implemented to theoretically verify adjustment ability of LGCM. A prototype based on SLM and Arduino UNO was fabricated and tested with proportional-integral-derivative (PID) to validate the effectiveness of the LGCM. The results illustrates that the vibration transmissibility in mismatched isolator at resonance frequency is decreased by 50 % with LGCM, which means that the resonance frequency can be decreased efficiently, and the isolation band is significantly broadened. The LGCM can be easily attached to any QZS systems, which can be regarded as a general patch for the bug of load-mismatch and is conducive to broaden the load-variable applications of QZS isolators.

Quasi-zero stiffness interval optimization design and dynamics analysis of a new bi-directional horizontal isolation system

The quasi-Zero Stiffness (QZS) isolation system is a typical nonlinear isolation system, which has high static stiffness characteristics to improve the bearing capacity and deformation resistance, and its low dynamic stiffness characteristics can reduce the inherent frequency of the system to realize a wider vibration isolation frequency band, so it has a more excellent low-frequency vibration isolation performance compared with the linear system. In this paper, a horizontal QZS isolator is constructed based on a pre-compressed oblique spring system, and two sets of the horizontal QZS isolators are mechanically assembled to work together to achieve a bi-directional horizontal QZS isolation system. Considering that the construction of two sets of horizontal vibration isolators is approximately the same, we focus on one of the isolators for the static analysis and derive the parameter conditions to be satisfied for achieving quasi-zero stiffness characteristics. We considered the effect of each adjustable parameter of the horizontal vibration isolator on the mechanical performance of the QZS system, and sought to optimize the QZS interval to improve the vibration isolation performance. A comparative study of the dynamical properties between the QZS system with ordinary and optimized parameters, as well as the equivalent linear system, is further carried out by means of nonlinear approximate analysis. Finally, the dynamic characteristics of the bi-directional horizontal QZS system and the equivalent linear system are compared by shaker tests on the prototype device, which proved the excellent vibration isolation performance of the proposed QZS isolation system.

A novel isolation system with enhanced QZS properties for supporting multiple loads

Various quasi-zero stiffness (QZS) isolators with high-static and low-dynamic stiffness (HSLDS) play an important role in effectively attenuating vibrations within the low-frequency range. Most existing QZS isolators can effectively achieve low-frequency vibration isolation under a certain load capacity, but cannot achieve excellent isolation performance for other load capacities. Hence, in this study, a novel isolation system composed of n series-arranged rhombic QZS elements for different supporting loads is proposed to explore its benefits in achieving ultra-low frequency vibration isolation. The novelty of the present design lies in the ability to support multi-load levels while maintaining multiple enhanced QZS properties by conveniently connecting QZS rhombic elements in series. The piecewise static stiffness responses are theoretically analyzed for multiple enhanced QZS characteristics. Nonlinear restoring forces are simulated by ADAMS to verify the theoretical results, which demonstrates that the static behavior of the proposed isolation system has multiple enhanced QZS behaviors. By employing the harmonic balance method (HBM), the nonlinear dynamic equation is formulated and subsequently solved to determine the vibration transmissibility. The vibration transmissibility of the novel isolation system with multiple QZS properties under different key parameters including the supporting load or static equilibrium position, base excitation amplitude, and damping coefficient are calculated. Numerical results demonstrate that the proposed isolation system can achieve superb ultra-low frequency and even full-band vibration isolation performance with a guaranteed stable equilibrium for different loads. The presented design provides new insights into ultra-low frequency passive vibration isolation required in various engineering fields.

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.

Integrated vibration isolation and actuation via dual nonlinear stiffness regulation

Integrating vibration isolation and actuation is superior, enabling enhanced vibration isolation performance while attaining controllable load position and attitude. Herein, a novel actuatable quasi-zero stiffness (QZS) vibration isolator (AQVI) is proposed and systematically investigated. The stiffness nonlinearization for QZS is fulfilled by paralleling nonlinear electromagnetic negative and positive stiffness structures. This configuration gives rise to an interesting behavior, that is, the rated load and equilibrium position are tailorable via dual nonlinear stiffness regulation, rendering the load actuatable without a trade-off with the QZS characteristic. The comprehensive static investigation is implemented to fully reveal and verify the dual nonlinear stiffness regulation mechanism. Dynamic governing equations are derived and solved in the cases of dwell and actuation, and it is found that the AQVI is capable of isolating broadband vibrations and tracking prescribed trajectories. Finally, an experimental apparatus is built to evaluate the vibration isolation performance and examine the effectiveness of the load actuation. The sweep excitation test demonstrates that the AQVI has good vibration isolation performance, exemplified by a low resonant frequency of 2.5 Hz and a small isolation starting frequency of 3.6 Hz. The load actuation test validates that the AQVI under open-loop control is competent to actuate the load following the desired trajectory while retaining excellent vibration attenuation. The proposed AQVI provides a novel paradigm for devising QZS isolators that are insensitive to the load and working point, shedding promising light on applications requiring integrated vibration isolation and actuation.