Quasi-zero Stiffness Research Articles

An Archetypal Vibration Isolator with Quasi-zero Stiffness in Multiple Directions

To avoid the failure under the longitudinal, shear, and mixed wave from earthquake, an archetypal vibration isolator based on a smooth and discontinuous (SD) oscillator is proposed. This model comprises a lumped mass mounted by a vertical spring and a horizontal elastic continuum, which separately provides positive and the negative stiffness forming the stable quasi-zero stiffness (SQZS) in all vertical and horizontal directions. The equation of motion is formulated by employing the Lagrange equation, and the SQZS condition is obtained by optimizing the geometrical parameters of the system. The analysis shows that the system admits remarkable performance in vibration isolation with low resonant frequency and a large stroke of SQZS interval. The results also demonstrate the system has improved aseismic behaviour under the complex excitation of seismic wave significantly.

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.

Dynamic Analysis of Quasi-Zero Stiffness Pneumatic Vibration Isolator

This paper focuses on analyzing the dynamic response of an innovated quasi-zero stiffness pneumatic vibration isolator (QZSPVI) using two mechanisms, including wedge and semicircle cam. Different from other studies relating quasi-zero stiffness isolation system, the pneumatic cylinder in this paper works as an air spring in order to easily adjust the dynamic stiffness of the proposed system according to the change of the isolated load through regulating the pressure. Firstly, the dynamic stiffness of the QZSPVI will be analyzed. Then, the condition for which the minimum dynamic stiffness is quasi-zero around the equilibrium position is also determined. The fundamental resonance response of the QZSPVI subjected to the externally harmonic force is analyzed through multi-scale method and the numerical simulations are verified. Secondly, due to exiting relative sliding frictional phenomenon between the cylinder and piston, instead of an experiment, another key content of this work is to identify the friction force model of the cylinder through virtual prototyping model. From this identified result, the complex dynamic response of the QZSPVI and coexistence of multiple solutions will be discovered by realizing the direct integration of the original dynamic equation through using the 5th-order Runge–Kutta algorithm. The analysis and simulation results clearly show the advantages of the proposed model against the equivalent pneumatic vibration isolator (EPVI), which only employs the wedge mechanism. This research will offer a useful insight into design and QZSPVI in practice.

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.

A Novel Low Stiffness Air Spring Vibration-Isolation Mounting System

Quasi-zero-stiffness (QZS) structures offer substantial practical benefits for facilitating the essential support and isolation of vibrational source loads aboard modern marine vessels. In order to design a compact QZS system of high bearing capacity, the article proposes a low stiffness air spring (LSAS) vibration-isolation mounting system composed of both vertical and lateral air springs. The vertical air springs support the load and isolate vibrations in the vertical direction, while the lateral air springs support the load and isolate transversal vibrations. Theoretical analyses based on a simple two-dimensional, single degree of freedom model demonstrate that the proposed novel LSAS design decreases the degree of stiffness in the support structure that would otherwise be induced by introducing lateral air springs and accordingly increases the vibration isolation effect. Moreover, optimization of the air spring parameters enables the lateral air springs to provide negative stiffness and thereby realize QZS characteristics. Experimental testing based on prototypes of a standard air spring mounting system and the proposed LSAS mounting system demonstrates that the stiffness of the proposed system is about 1/5 that of the standard system. Accordingly, the proposed structure design successfully alleviates the undesirable influence of lateral air springs on the stiffness of the mounting system.

Design and testing of a parabolic cam-roller quasi-zero-stiffness vibration isolator

Circular cam-roller (CCR) quasi-zero stiffness (QZS) vibration isolators have been extensively studied. As the CCR isolator can only achieve low stiffness in a very small range and cannot withstand excitation with large amplitude, study on other cam profiles has become interests. This paper investigates a parabolic cam-roller (PCR) QZS vibration isolator. Theoretical formulations of the PCR QZS isolator are derived in detail and the condition of PCR isolator outperforming CCR one is obtained. Design parameters are analyzed and then the optimal design is presented. A prototype of the PCR QZS vibration isolator is fabricated and tested; the corresponding CCR QZS and linear isolators are also experimentally evaluated. In comparison with CCR QZS isolators, the proposed PCR QZS isolators can withstand force and displacement excitations with larger amplitudes in the QZS region. The experimental results validate the present formulation and show that vibration isolation performance of the proposed PCR QZS isolator is much better than that of the CCR QZS isolator and that of the corresponding linear isolator. In comparison with the CCR QZS isolator, the present PCR QZS isolator can have lower stiffness in a wider region around the equilibrium position and lower transmissibility.

Effect of damping nonlinearity on the dynamics and performance of a quasi-zero-stiffness vibration isolator

Quasi-zero-stiffness (QZS) vibration isolators that take advantage of stiffness nonlinearity are commonly studied with linear damping elements. This paper concerns the effects of damping nonlinearity on their dynamics and performance. Geometric nonlinear damping originating from horizontal and rotational dampers is considered. Analytical expressions for displacement and force transmissibility and stability of the isolator are derived using the harmonic balance method and, especially for large-amplitude excitation, numerical continuation. The beneficial effect of nonlinear damping on the removal or minimization of unwanted isolated subharmonic branches is shown. Metrics are defined to assess the performance of the QZS isolator. Results indicate that, for both small and large-amplitude base excitation, increasing nonlinear damping can effectively suppress peak transmissibility; however, as base excitation level increases, larger nonlinear damping increases transmissibility at intermediate to high frequencies. On the other hand, results reveal that for all levels of force excitation, force transmissibility at higher frequencies is not dependent on the variations of nonlinear damping and is just a function of the linear damping. Whatever the input level, the peak transmissibility of the forced QZS isolator can be reduced by increasing nonlinear damping.

Magnetically modulated sliding structure for low frequency vibration isolation

Magnetically modulated sliding structure (MMSS) is proposed and systematically investigated in this paper. The MMSS consists of the sliding beam and a pair of repulsive magnets. The sliding beam can provide negative stiffness, which can be modulated by a pair of repulsive magnets (hardening positive stiffness). The static analysis is completed to fully clarify the modulation mechanism. With the modulation of magnets, the sliding beam can exhibit favorable high-static-low-dynamic stiffness (HSLDS). The dynamic model of the MMSS is developed to evaluate its response when subject to base excitation. The displacement transmissibility is derived by the harmonic balance method (HBM). Transmissibility curves show that the MMSS isolator possesses a low resonant frequency and can isolate vibration in a wide frequency range. The principle prototype is fabricated and tested. The effectiveness of the modulation mechanism in realizing quasi-zero stiffness (QZS) is verified by static experiment. Dynamic tests under periodic, sweep and random excitation demonstrate that the isolator exhibits excellent low frequency isolation performance and the vibration exceeding 4 Hz can be effectively isolated. The MMSS system provides a new approach to solve the problem of low frequency vibration isolation. The modulation mechanism, that is, utilizing hardening stiffness to modulate negative stiffness, is of reference significance for the design of HSLDS isolators.

Fuzzy PID Control of Nonlinear Vibration Isolator with Parallel Electromagnetic Negative Stiffness

A fuzzy PID control strategy for quasi-zero stiffness (QZS) isolator which connects the pneumatic spring (PS) and the electromagnetic negative stiffness mechanism (ENSM) in parallel to suppress low-frequency vibration is proposed in this paper. First, the restoring force of PS and the electromagnetic force of the ENSM are derived. Secondly, the static analysis of the isolation system is carried out, and the analytical expressions of stiffness and restoring force of the vibration isolation system is obtained. The possibility of the vibration isolator reaching the QZS state is explained. Then, to obtain a better isolation effect, the optimal current of the coil is found according to the designed fuzzy PID control strategy. Finally, the simulation result shows that the isolation frequency band of the isolation system under fuzzy PID control and PID control is widened, and the vibration isolation performance under fuzzy PID control reaches more than 85% under different excitation frequencies. Control effect and vibration isolation performance under fuzzy PID control are better.

Design and Analysis of a Novel Quasi-Zero Stiffness Isolator under Variable Loads

The designed load of most quasi-zero stiffness (QZS) isolators is constant. The isolation performance will drop sharply once the load changes. A novel QZS isolator that can adapt to variable loads is proposed in this paper to improve the range of application of the isolator. The isolator is designed by paralleling the electromagnetic spring (ES), which provides negative stiffness, and the pneumatic spring (PS), which provides positive stiffness. The positive and negative stiffness can be adjusted by changing the pressure and coil current, which provides the possibility for the isolator to adapt to variable loads. This paper derived the conditions for the isolation system to obtain QZS characteristics, proposed the dynamic model of the isolation system, derived and verified the analytical expressions of the amplitude-frequency response and force transmissibility (FT), and discussed the change of FT and displacement transmissibility(DT) under different loads. Theoretical analysis shows that changing the pressure and coil current in the same proportion can maintain the superior low-frequency isolation performance when the load changes, thanks to the preservation of the QZS characteristics of the system after adjusting the pressure and coil current. Finally, the simulation results fg and isolation frequency band over the linear isolation system and PS isolation system. Furthermore, the proposed isolator can be adjusted online.

Bionic paw-inspired structure for vibration isolation with novel nonlinear compensation mechanism

Inspired by the compensation effect of fat pad on toes in a paw of digitigrade, a unique paw-inspired structure (PIS) is proposed and systematically investigated to explore its advantages in passive vibration isolation. The PIS consists of two key parts, one is the toe-like structure (TLS) simulated by two rods and a spring, and the other is fat pad mimicked by a pair of repulsive magnets. Based on the principle of virtual work, the static stiffness characteristics of the TLS are firstly analyzed. Then, the stiffness compensation mechanism of fat pad to toe is comprehensively studied. The hardening stiffness of the fat pad can compensate the negative stiffness of the TLS so that the PIS can realize quasi-zero stiffness (QZS) over large displacement range. It is for the first time to reveal this nonlinear stiffness compensation mechanism, which is essentially different from the conventional realization of QZS (connecting negative stiffness mechanism and linear spring in parallel). A dynamic model is established to estimate the vibration isolation performance. The displacement transmissibility derived by harmonic balance method (HBM) indicates that the PIS can achieve low resonance frequency and wide effective vibration isolation frequency band. Static tests are completed to verify effectiveness of the stiffness compensation mechanism. Tests under different external excitations (including periodic, sweep and random) show that the PIS can effectively suppress frequency components above 4 Hz. The PIS provides a new low-frequency vibration isolation method with high application prospects. And the proposed nonlinear stiffness mechanism can also be extended as a guideline to design nonlinear vibration isolators.

Bistable inclined beam connected in series for quasi-zero stiffness

This paper investigates a structure system that expresses stable and controllable quasi-zero stiffness in an integrated form, which is based on inclined bistable beams connected in series. This paper shows that interaction between the connected beams and their nonlinear axial stiffness always leads to a plateau trajectory in its force-displacement curve with very low tangential stiffness. The plateau part of the force-displacement occurs while each of the connected beam snaps through sequentially and ends when all of the beams are going though hardening behavior. A series of tests were conducted to validate this behavior. A numerical model capable of predicting the behavior is developed. Studies were performed based on the model for this kind of structure with different geometric configuration and details of coupling links. The results show that in addition to being able to achieve quasi-zero stiffness of an integrated structures, this kind of structure has increased initial stiffness and loading capacity compared with traditional bistable structures subjected to similar limitations of extreme strains.

X-shaped mechanism based enhanced tunable QZS property for passive vibration isolation

A novel spring arrangement based on the X-shaped anti-vibration structure with tunable contact mechanism (NXSC) is proposed to explore much better low-frequency vibration isolation performance. An enhanced quasi-zero-stiffness (QZS) with large stroke is obtained by tuning contact position between the horizontal springs and vertical fixed rods. The loading capacity and working range of the NXSC structure can be extended by 2, 3 times compared with classical X-shaped structures. The proposed NXSC structure is adjustable to different loading requirements and resonant frequencies, and excellent vibration isolation performance can be achieved readily by tuning the contact parameter. Three types of the NXSC structure with different contact modes are designed. The effects of structural parameters on the loading capacity and QZS zone are analyzed. By tuning the contact parameter via special tuning mechanisms, the negative stiffness can be compensated completely to ensure the stability of isolation systems. Comparisons with a typical spring-mass-damper (SMD) isolator and an existing QZS isolator exhibit that the stiffness-displacement curve of the NXSC structure is much more adjustable with significantly extended QZS in a wider displacement range, and does not sacrifice loading capacity. Moreover, the NXSC structure is less sensitive to excitation amplitude than the traditional QZS isolator, and it does not produce frequency jump phenomenon and softening and hardening stiffness effects. Experiments are implemented to verify the theoretical result and demonstrate that the proposed NXSC structure possesses superior vibration isolation performance and can effectively attenuate vibration at low-frequency range. This NXSC structure presents a new and efficient way for manipulating beneficial nonlinearity based on the X-shaped structure for better engineering performance.

Vibration control of an unbalanced system using a quasi-zero stiffness vibration isolator with fluidic actuators and composite material: An experimental study

In this study, a new type of vibration isolator based on fluidic actuators and a composite slab was tested experimentally with an unbalanced disturbance. Quasi-zero stiffness vibration isolation techniques are advanced and provide effective isolation performance for non-nominal loads. The isolation performance of the proposed isolator was compared to that of a nonlinear vibration isolator equipped with fluidic actuators and a mechanical coil spring (NLVIFA). The NLVIFA system is better suited to non-nominal loads; however, the mechanical spring axial deflection leads to limited amplitude reduction in the system. To address this issue, a cross buckled slab was developed to replace a mechanical coil spring for absorbing vertical deflection by transverse bending, which is made of a specially developed composite material of Basalt fiber reinforced with epoxy resin and enhanced with graphene nano pellets. This current study was concerned with the theoretical analysis and experimental investigations of the proposed nonlinear vibration isolator with fluidic actuators and composite material (NLVIFA-CM), which performs under quasi-zero stiffness characteristics. Because of its reduced axial deflection, the theoretical and experimental results show that the NLVIFA-CM system outperforms the NLVIFA system and other linear type vibration isolators in terms of isolation performance. Furthermore, the proposed vibration isolator makes a significant contribution to low-frequency vibration.

Lightweight origami isolators with deployable mechanism and quasi-zero-stiffness property

Efficient vibration isolation is an important problem in engineering. Nonlinear isolators with quasi-zero-stiffness (QZS) property have been studied for many years due to their beneficial vibration isolation performance. However, such isolators are typically undeployable, as well as large and heavy in many cases, while designing a structure that is deployable and lightweight is required for many practical applications, especially for aerospace engineering. Origami has recently found their application in various research areas, including engineering. This ancient art of paper folding can be used to construct novel nonlinear isolators that can overcome the aforementioned shortcomings of the previously proposed isolators. In this work, a lightweight nonlinear vibration isolator with deployable mechanism and QZS property is proposed by using the Kresling origami modules (KOMs). The QZS property is achieved by utilizing the supercritical pitchfork bifurcation, which provides theoretical foundation to guide the design of such an isolator. The QZS KOMs with automatic deployment mechanism and the conditions under which the isolator can be fully folded are investigated. Subsequently, by establishing the dynamic model of the isolator, the response of the proposed isolator under base's excitation is obtained by using the averaging method and validated by the simulation of a virtual truss prototype in ADAMS. For the validated model, parametric studies are performed to understand the effects of various design parameters and arrangements (series and parallel) on the vibration isolation performance of the proposed isolator, while an ultra-low frequency vibration isolation and, for some cases, vibration isolation covering the full frequency range are shown to be present for the system. Remarkably, the performance of the proposed isolator is significantly enhanced by connecting the KOMs in series. With the developed theoretical framework and findings from this work, it is demonstrated that origami provides a new way to design effective nonlinear QZS isolators suitable for aerospace applications.

Research and Development of Applied Devices utilizing the Buckling Properties of Tape-shaped Shape Memory Alloy Elements

An elongated Shape memory alloys (SMAs) elements which shows superelastic properties can exhibit the quasi-zero or negative stiffness during post-buckling deformation. Since the buckling deformation is recovered by the superelastic effect upon unloading, the quasi-zero or negative stiffness can be used continuously. Our research group has devised, studied and reported on passive vibration isolator devices that utilize this property, but this property can be applied not only to passive vibration isolator but also to various other possible applications. This paper reports on the characteristics of a force-limiting device using the buckling properties of shape memory alloy elements, which was devised and prototyped by our research group. We also report on the newly devised convex-tape shape memory alloy element and the movement characteristics of a rehabilitation mechanism using its buckling characteristics.

Low-frequency sound insulation performance of novel membrane acoustic metamaterial with dynamic negative stiffness

For improving the low-frequency sound insulation properties of membrane/plate structures, a new quasi-zero stiffness membrane acoustic metamaterial with dynamic magnetic negative stiffness is proposed. When the equivalent magnetic charge theory is used to investigate the dynamic magnetic negative stiffness, a theoretical model of proposed metamaterial with finite dimension is established based on the Galerkin method. Through a combination of theoretical analysis, numerical simulation and experimental measurement, the low-frequency (1–1000 Hz) sound insulation performance of the metamaterial is investigated from several perspectives, including structural modality, vibration mode, average velocity, phase curve, equivalent mass density, and equivalent spring-mass dynamics model. The results show that at a certain initial membrane tension, the decreasing of the magnetic gap or the increasing of the residual flux density can increase the dynamic magnetic negative stiffness. This in turn leads the peak frequency to decrease and the bandwidth of sound insulation to increase, thus achieving effective low-frequency sound insulation over a wide frequency band. Further, when the magnetic gap is larger than the second critical magnetic gap and smaller than the first critical magnetic gap, the first-order modal resonance of the metamaterial disappears, and the corresponding value of sound insulation valley increases significantly, thus demonstrating superior sound insulation effect in a wide frequency band. The proposed method of using dynamic magnetic negative stiffness to improve low-frequency sound insulation valleys due to modal resonance provides useful theoretical guidance for designing membrane/plate type low-frequency sound insulation metamaterials.

Low-frequency sound insulation performance of novel membrane acoustic metamaterial with dynamic negative stiffness

For improving the low-frequency sound insulation properties of membrane/plate structures, a new quasi-zero stiffness membrane acoustic metamaterial with dynamic magnetic negative stiffness is proposed. Upon applying the equivalent magnetic charge theory to derive the dynamic magnetic negative stiffness, a theoretical model of proposed metamaterial with finite dimensions is established based on the Galerkin method. Through a combination of theoretical analysis, numerical simulation and experimental measurement, the low-frequency (1—1000 Hz) sound insulation performance of the metamaterial is investigated from several perspectives, including structural modality, vibration mode, average velocity, phase curve, equivalent mass density, and equivalent spring-mass dynamics model. Results show that, at a certain initial membrane tension, decreasing the magnetic gap or increasing the residual flux density can increase the dynamic magnetic negative stiffness. This in turn leads to decreased peak frequency and enlarged bandwidth of sound insulation, thus achieving effective low-frequency sound insulation over a wide frequency band. Further, when the magnetic gap is larger than the second critical magnetic gap and smaller than the first critical magnetic gap, the first-order modal resonance of the metamaterial disappears, and the corresponding value of sound insulation valley increases significantly, thus demonstrating superior sound insulation effect with wide frequency band. The proposed method of using dynamic magnetic negative stiffness to improve low-frequency sound insulation valleys due to modal resonance provides useful theoretical guidance for designing membrane/plate type low-frequency sound insulation metamaterials.

Nonlinear compensation method for quasi-zero stiffness vibration isolation

Various quasi-zero stiffness (QZS) vibration isolators have been emerged in recent years and applied successfully in low-frequency vibration isolation. However, in most cases, the general approach to achieving QZS is still limited to compensating the negative stiffness of the bistable structure by linear springs. Here, a nonlinear compensation method (NCM) for realizing QZS is developed and the corresponding methodology is systematically investigated. Specifically, for a certain negative stiffness structure (not limited to bistable structure), QZS can be obtained by utilizing hardening stiffness to compensate. A confirmatory QZS vibration isolation system is established to fully verify the effectiveness of the NCM. The confirmatory system exploits rhombus structure to generate nonlinear negative stiffness, which can be compensated by nonlinear positive stiffness (provided by repulsive magnets). The static analysis is completed to reveal the inherent stiffness compensation mechanism. The dynamic and experimental results demonstrate that the proposed QZS system has low resonant frequency and wide effective vibration isolation frequency band. The NCM has reference significance in realizing QZS and is beneficial to develop diversified low-frequency vibration isolators.

An Improved Structural Analysis Method for Isolator with Quasi-Zero-Stiffness Characteristic

A typical quasi-zero-stiffness (QZS) vibration isolator consisting of a vertical spring and two oblique springs has been widely researched on its static and dynamic characteristics. A general criterion for determining structural parameters of QZS isolator is to achieve low nondimensional stiffness around the equilibrium position. However, lower nondimensional stiffness of linear isolator means lower isolation frequency, which may be invalid on QZS isolator. Because there is an implicit relationship between geometric parameter and stiffness ratio of QZS isolator, this study presents an improved optimization criterion for determining the optimal structural parameters of the typical QZS isolator. The optimization criterion is that the QZS isolator has the maximum displacement range around the equilibrium position without exceeding given natural frequency, rather than given nondimensional stiffness. The results show that isolator with these optimal parameters can achieve lower stiffness around the equilibrium position and better vibration isolation performance. Furthermore, an extended QZS isolator consisting of vertical spring with fixed stiffness and prestressed oblique springs is discussed to further improve stiffness characteristic. Better stiffness performance can be obtained when the prestressed oblique springs have softening stiffness and the exponent of the nonlinear stiffness is 2. Considering the existence of friction in practical application, the influence of friction on both static and dynamic characteristics is investigated. The analysis reveals that friction has little influence on its stiffness characteristic around the static equilibrium position and friction damping produced by friction affects the response amplitude and resonant frequency in dynamics.