Low-frequency Vibration Isolation Research Articles

Ultra-low frequency and broadband flexural wave attenuation using an inertant nonlinear metamaterial beam

Attenuation of elastic waves in the extremely low frequency range is a considerable challenge. While linear acoustic metamaterials can manipulate elastic waves, their effectiveness is often limited to a narrow frequency range. The present paper proposes a novel inertant nonlinear metamaterial beam to address the challenging problem of the ultra-low frequency broadband flexural wave attenuation. The amplitude-frequency response and dispersion relations of the flexural waves are obtained using the first-order harmonic balance method, where four different resonant units are investigated and the resulting band gaps are compared. Finite element (FE) simulations are also conducted to evaluate the transmission spectra of the flexural vibration through a finite metamaterial beam. The good consistency between the band gaps predicted by the analytical model and the FE simulation verifies the correctness and effectiveness of the developed analytical approach. The results of this study demonstrate that introducing the inertance and softening nonlinearity into the resonant units can significantly widen the flexural wave band gaps within the low-frequency range. This finding provides a viable solution for engineering applications that require low-frequency vibration suppression and isolation.

Design of piezoelectric quasi— zero—stiffness metastructures for improved low—frequency vibration isolation

Abstract In this paper, a novel type of piezoelectric quasi–zero stiffness (QZS) metastructure is proposed and the improved vibration isolation performance is investigated. A piezoelectric QZS metastructure is composed of curved beams covered with piezoelectric macro–fiber composite patches, to which digital circuits are connected. Based on the principle of minimum potential energy and the mode superposition method, the constrain on the geometry and material parameters of the piezo–curved beams to achieve QZS is given. According to this design criterion, 1D, 2D and 3D piezoelectric QZS metastructures are designed, and their improved low–frequency vibration isolation characteristics are comprehensively analyzed through theoretical, numerical and experimental studies. It is demonstrated that by optimizing the parameters of the resonant transfer functions implemented in the digital circuits, high–level damping localized near the first resonant peak can be introduced into the curved beams. As a result, the resonant peaks of the metastructures can be reduced without compromising the isolation performance beyond those peaks.

Inverse design of acoustic metamaterial-based vibration control for offshore wind turbines

This paper presents an inverse design approach for mechanical metamaterial turbines utilising a deep learning algorithm. We first establish a theoretical model for metamaterial turbines using the spectral element method to analyse their vibration characteristics. Subsequently, we predict the vibration transmission properties of these turbines and achieve on-demand inverse design of metastructures through a fully connected deep-learning neural network model. The efficacy of the forward prediction and reverse design network models is validated using an inverse neural network. Our results demonstrate a strong agreement between the predicted and target values, affirming the feasibility of employing deep learning for on-demand meta-turbine design. This intelligent design approach holds promise for expediting and enhancing the design of metamaterials tailored for low-frequency vibration isolation in engineering structures.

Programmable Quasi-Zero-Stiffness Metamaterials

Quasi-zero-stiffness (QZS) metamaterials have attracted significant interest for application in low-frequency vibration isolation. However, previous work has been limited by the design mechanism of QZS metamaterials, as it is still difficult to achieve a simplified structure suitable for practical engineering applications. Here, we introduce a class of programmable QZS metamaterials and a novel design mechanism that address this long-standing difficulty. The proposed QZS metamaterials are formed by an array of representative unit cells (RUCs) with the expected QZS features, where the QZS features of the RUC are tailored by means of a structural bionic mechanism. In our experiments, we validate the QZS features exhibited by the RUCs, the programmable QZS behavior, and the potential promising applications of these programmable QZS metamaterials in low-frequency vibration isolation. The obtained results could inspire a new class of programmable QZS metamaterials for low-frequency vibration isolation in current and future mechanical and other engineering applications.

A new magnetic negative stiffness mechanism: A case study of Fast Steering Mirror for quasi-zero stiffness vibration isolation

Quasi-Zero Stiffness (QZS) is essential for low-frequency passive vibration isolation, with the negative stiffness mechanism (NSM) being pivotal for achieving QZS. Mechanical spring-based NSMs often face issues like contact friction, parasitic high-frequency modes, and stiffness nonlinearity. This paper presents a new magnetic NSM designed to overcome these challenges effectively. The mechanism is applied to a Fast Steering Mirror (FSM) as a case study, enhancing its vibration isolation performance. Initially, a torque model for the magnetic NSM is established, exploring the impact of various structural dimensions on torque and nonlinear issues. The magnetic NSM features adjustable negative stiffness and a large, adjustable linear working range. Experiments were designed to validate the principle of the magnetic NSM and its effect on the QZS FSM’s vibration isolation performance. The experimental results confirm the accuracy of the magnetic NSM principle. The QZS FSM stiffness is significantly reduced to quasi-zero stiffness, resulting in a decrease of the resonance peak from 20.1 to −12.8 dB and lowering the minimum suppressible vibration frequency from 54.63 to 3.44 Hz, thereby enhancing the vibration isolation performance of the QZS FSM.

Design and static and dynamic analysis of floor vibration isolators for high-speed train.

With the increasing speed of high-speed train, it is more and more difficult to reduce the vibration and noise inside the train. The floor of the train, as a carriage component in direct contact with passengers, is of great significance to improve its vibration and sound isolation performance to ensure the comfort of passengers. In this article, a floor vibration isolator with quasi-zero stiffness is designed based on the dimensional parameters of the traditional floor vibration isolator, and the vibration isolation performance is analyzed by the finite element model of the floor vibration isolator from the static and dynamics aspects, respectively. The load-displacement curves of the floor vibration isolator are obtained through static simulation calculations, and the dynamic analysis of the floor vibration isolator is carried out by simulation methods, which verifies the low-frequency vibration isolation performance of the floor vibration isolator under different working conditions, and the vibration isolator has a good prospect for development.

Tunable low-frequency broadband band gap in nonlinear locally resonant metamaterial inspired by sarcomere structure

Since traditional locally resonant metamaterials (LRMs) cannot achieve a broadband band gap in the low-frequency band, the suppression and isolation of low-frequency broadband vibration has always been a difficult problem in the field of vibration control. Therefore, in this paper, inspired by the structure of the sarcomere, a novel nonlinear LRM is proposed, aiming to open a wider band gap in the low-frequency band. Firstly, a statics model of the nonlinear local resonator (LR) is established to explore the mechanical nonlinear characteristics of the structure with different geometric parameters. And the inflection point fitting method is used to approximate the nonlinear statics model of nonlinear LR. Then a dynamics model was established, the nonlinear dispersion relationship of the infinite periodic system was obtained by Bloch's theorem and l-P perturbation method. And an analytical investigation of the theoretically calculated band gap is conducted through the band gap ratio and relative band gap width. In addition, according to the influence of different structural parameters on the real and imaginary parts of the wave vector, the regulation rules and mechanisms for nonlinear LRM to open low-frequency broadband band gaps are revealed. Finally, the Runge-Kutta method was used to numerically calculate the vibration transmissibility curve of the nonlinear LRM composed of a limited number of nonlinear LRs. And the correctness of the theoretically calculated band gap was verified. The research results provide theoretical support for the application of nonlinear LRMs in the suppression and isolation of low-frequency broadband vibrations.

Simultaneous low-frequency vibration isolation and energy harvesting via attachable metamaterials

In this study, we achieved energy localization and amplification of flexural vibrations by utilizing the defect mode of plate-attachable locally resonant metamaterials, thereby realizing compact and low-frequency vibration energy suppression and energy harvesting with enhanced output performance. We designed a cantilever-based metamaterial unit cell to induce local resonance inside a periodic supercell structure and form a bandgap within the targeted low-frequency range of 300–450 Hz. Subsequently, a defect area was created by removing some unit cells to break the periodicity inside the metamaterial, which led to the isolation and localization of the vibration energy. This localized vibration energy was simultaneously converted into electrical energy by a piezoelectric energy harvester coupled with a metamaterial inside the defect area. Consequently, a substantially enhanced energy harvesting output power was achieved at 360 Hz, which was 43-times higher than that of a bare plate without metamaterials. The proposed local resonant metamaterial offers a useful and multifunctional platform with the capability of vibration energy isolation and harvesting, while exhibiting easy handling via attachable designs that can be tailored in the low-frequency regime.

A quasi-zero-stiffness vibration isolator inspired by Kresling origami

Vibration isolators are widely used to mitigate undesirable vibrations in engineering systems and structures, but low-frequency vibration isolation remains a challenge. Origami-inspired structures, with their tunable stiffness and transformative capabilities, offer potential for vibration isolation. Inspired by conical Kresling origami, this study proposes a quasi-zero-stiffness vibration isolation system. Static analysis of the origami structure reveals that the system exhibits near-zero dynamic stiffness at the static equilibrium position, while maintaining static stiffness during the load-bearing process. The amplitude-frequency characteristic formula and vibration transmissibility formula are derived using the harmonic balance method. The effects of varying damping ratios and excitation amplitudes on the amplitude-frequency and transmissibility curves are examined. It is shown that the vibration isolation range increases with the number of layers. A comparison of the system's response to harmonic vibrations under different compressive deformations highlights the effectiveness of the origami quasi-zero-stiffness system as a vibration attenuator. Compared to existing quasi-zero-stiffness dampers, the origami-inspired system features a wider isolation frequency band, a lower initial isolation frequency, and reduced vibration transmissibility, demonstrating superior isolation performance, particularly at low frequencies.

Nonlinear anti-vibration compliant mechanism with inertia amplification

This paper presents a novel nonlinear anti-vibration compliant mechanism with a coupled inertia amplification (NAVCM-IA) for low frequency vibration isolation. This compliant mechanism consists of three-dimensional helical rods with stiffness nonlinearities, and an attached horizontally-installed inertia disc which performs as an inertia amplification. With this unique design, beneficial nonlinear stiffness can be achieved, which reduce the dynamic stiffness at equilibrium position and improve the vibration isolation performance at low frequency range. Moreover, the inertia amplification driven by the compliant mechanism achieves an apparent high dynamic mass and, accordingly, a low resonance frequency. The nonlinear compliant mechanism with a coupled inertia amplification is validated by experimental prototypes for their special nonlinear features. The proposed NAVCM-IA is a unique passive and adjustable low frequency anti-vibration solution in extensive engineering applications.

An approach for realizing lightweight quasi-zero stiffness isolators via lever amplification

Quasi-zero stiffness (QZS) vibration isolators exhibit excellent performance in low-frequency vibration isolation but require the negative stiffness to be consistent or close to the positive stiffness, which may lead to an excessively large volume or weight of the negative stiffness mechanism. In this paper, a lightweight QZS (L-QZS) vibration isolator using the lever amplification mechanism is developed, theoretically investigated, and experimentally verified. The negative stiffness can be amplified by one order of magnitude through the amplification effect of the lever structure, enabling a lower negative stiffness to compensate for the positive stiffness. Meanwhile, the lever increases the inertia effect of the negative stiffness structure, leading to an increase in the system’s effective mass and further reducing the resonance frequency. Results indicate that with a small negative stiffness, the isolation bandwidth of L-QZS isolators is significantly enlarged. The transmissibility at high frequencies of the L-QZS isolator tends to a certain value, which is mainly determined by the lever ratio and the tip mass of the lever. Furthermore, the negative stiffness can be controlled by adjusting the lever ratio, providing a viable method for matching various positive stiffnesses in engineering applications.

Nonlinear interactions of an n-layer X-shape low-frequency vibration isolator equipped with a nonlinear vibration absorber at 1:1 internal resonance: analytical and numerical investigations

This work addresses, for the first time, the nonlinear dynamics of an n− layers bioinspired X− shape low-frequency vibration isolation system equipped with a nonlinear vibration absorber. The comprehensive mathematical model governing the two-degree-of-freedom system has been derived using Lagrangian mechanics. The method of averaging was applied to obtain an accurate analytical solution for the derived mathematical model. Utilizing the established analytical solution, the dynamical characteristics of the X− shape vibration isolator have been explored both as a single-degree-of-freedom system and after coupling with the proposed vibration absorber, as a two-degree-of-freedom system. The influence of different system parameters, including the number of structure layers, the initial inclination angle, the X− shape rod length, and the absorber stiffness and damping coefficients, on the vibration isolation performance has been investigated. The main findings indicate that while the single-degree-of-freedom X− shape low-frequency vibration isolator performs well in eliminating low-frequency vibration excitations, it exhibits strong vibration levels when the base excitation frequency exceeds the structure's natural frequency. Additionally, it was found that coupling a highly damped linear vibration absorber to the X− shape isolator not only eliminates the strong oscillations of the structure when subjected to high-frequency base excitations but also enhances the structure's low-frequency vibration isolation performance. Moreover, it was reported that integrating a nonlinear vibration absorber with either soft or hard spring characteristics instead of a linear one may degrade the vibration isolation performance of the structure rather than enhance it. Finally, numerical validation of all the analytical results was performed, which showed excellent correspondence with the analytical findings.

Active Composite Control of Disturbance Compensation for Vibration Isolation System with Uncertainty

The pointing and positioning accuracy of precision instruments in aerospace are often disturbed by low-frequency vibrations. An active/passive vibration isolation system is a feasible solution to suppress low-frequency vibrations. However, the vibration isolation performance of the active control strategy is seriously affected by the uncertainty of the system and the difficulty to meet the higher requirements of new-generation equipment. This paper proposes an active composite control (ACC) strategy for vibration isolation systems with uncertainty. The proposed ACC integrates feedforward control based on known systems and feedback control based on the Kalman filter for systems with uncertainty. Further, the derivation and stability analyses of the proposed ACC algorithm are provided, and the influence of system uncertainty on vibration isolation performance based on the proposed ACC is analyzed. Experimental verification is conducted and the experimental results confirm that the proposed ACC can effectively realize the low-frequency and wide-band vibration isolation for the system with uncertainty. Starting from 30 Hz, the vibration isolation performance of the proposed ACC with uncertainty is significantly improved than that of the ACC completely based on a deterministic system model.

Design of broad quasi-zero stiffness platform metamaterials for vibration isolation

Adaptability and reliability are challenges in designing vibration isolation structures, and mechanical metamaterials featuring broad quasi-zero stiffness (QZS) platforms are among the most promising candidates for addressing this issue. This paper proposes a novel design of vibration isolation metamaterials featuring a broad QZS platform to achieve vibration control in complex environments. The metamaterial unit cells are designed by integrating horizontal and diagonal beams based on the mechanism combining Euler buckling and flexural deformation. Herein, the component made of diagonal beams is configured to exhibit negative stiffness behavior, while the designed support components aim to relax the boundary constraints of the diagonal beam component, thereby mitigating the negative stiffness effect. By tuning the synergistic effects between horizontal and diagonal beams, QZS features can be achieved over a broad range of displacements. A combination of theoretical analysis, finite element method and experiment is employed to investigate the payload and QZS features of metamaterials comprehensively. Notably, the designed unit cell maintained a considerably broad QZS platform, with static experiments revealing that this platform accounts for approximately 55 % of the total loading range. Furthermore, the designed metamaterials exhibit excellent vibration isolation performance in the low-frequency range, with vibration experiments demonstrating that the unit cell can effectively shield vibrations across almost the entire range when the support mass corresponds to the QZS payload. The geometric parameters of the metamaterial configuration that influence the range of the QZS platform are also explored. In conclusion, the proposed mechanical metamaterials have a tunable and broad QZS platform with considerable potential for use in customized low-frequency vibration isolation applications.

Design and Vibration Isolation Investigation of a Load-Adjustable Quasi-Zero Stiffness Isolator

Quasi-zero Stiffness (QZS) isolators offer significant advantages in low-frequency vibration isolation. Nonetheless, the complexity of the structure and the limited load adaptability hinder the practical application of such isolators. Therefore, this paper proposes a novel load-adjustable QZS isolator based on a compliant mechanism. By integrating the positive stiffness of the curved beam and the negative one of the inclined beam, a comprehensive design strategy for the QZS flexible beam is introduced. The optimal geometric parameters of the structure are determined using a genetic algorithm, and the finite element simulations are employed to numerically validate the QZS characteristics of the structure as well as the low-frequency vibration isolation performance. Leveraging the same structural design and a kind of temperature-sensitive materials-Thermoplastic Polyurethane (TPU), a unit cell of load-adjustable QZS isolator controlled by electric heating is developed and fabricated via 3D printing. Static and dynamic tests are conducted to explore the QZS platform characteristics and vibration isolation performance of the isolator subjected to various voltage inputs. The results demonstrate that the QZS characteristics of the isolator can be effectively regulated by adjusting the input voltage, ensuring effective low-frequency vibration isolation under different loads. Moreover, the incorporation of serial and parallel arrangements of unit cells could further enhance the range of load adjustability. This study offers novel insights into the design of load-adjustable QZS isolators.

Nonlinear wire rope isolator with magnetic negative stiffness

The high-static-low-dynamic-stiffness (HSLDS) isolators have been widely employed to achieve low-frequency vibration isolation. However, traditional HSLDS isolators are prone to nonlinear jump phenomena due to the introduction of nonlinear stiffness characteristics, which will cause the performance deterioration under high excitation levels. To overcome this issue, inspired by the dry friction characteristic of wire ropes, the wire ropes are employed to design HSLDS isolators to suppress nonlinear jump phenomenon by introducing hysteretic damping in this paper. Therefore, a nonlinear wire rope isolator with magnetic negative stiffness is proposed to achieve HSLDS with hysteretic damping. The elastic force of wire rope and the magnetic force are modeled to obtain nonlinear restoring force, and then the dynamic model of the proposed isolator is established to investigate isolation performance. The equivalent beam element method is proposed to model wire ropes for obtaining dynamic characteristics by considering tensile and bending stiffnesses. Then, numerical simulation is performed to investigate the isolation performance of the wire rope isolators with different magnetic negative stiffnesses, and demonstrates that the proposed isolator can work in a higher excitation level than the isolator without dry friction of wire ropes. Moreover, experiments are carried out to show that the onset isolation frequency of the proposed isolator can be reduced by 66.7% compared with the wire rope isolator without magnetic negative stiffness. Therefore, it is demonstrated that the proposed wire rope isolator with magnetic negative stiffness has the preferable performance in low frequency isolation, and can improve the adaptability under a higher excitation level.

Performance Improvement of Three-Spring Quasi-Zero-Stiffness Isolator by Shape Memory Alloy Damper

Quasi-zero stiffness vibration isolators (QZSI) can effectively resolve the contradiction between the load bearing and the vibration isolation for low-frequency vibration systems. The three-spring QZSI is a classical QZSI. However, constrained by its geometrical relationship, the working stroke of the QZSI is limited, and the isolation performance will deteriorate when the displacement response is significant. To solve this question, the shape memory alloy (SMA) damper, characterized by lower secondary stiffness, partially replaces the positive-stiffness spring of the three-spring QZS isolator to widen its effective working stroke, which forms a novel SMA-QZSI. Based on a piecewise linear constitutive model of SMA, a theoretical model of the force–displacement relationship of SMA-QZSI is established. Subsequently, the approximate analytic amplitude–frequency response equation of the non-smooth nonlinear SMA-QZSI system under harmonic excitation is obtained by the average method and verified numerically. In addition, the effects of mechanical parameters of SMA springs and external excitation parameters on mechanical behaviors and low-frequency isolation performance of the SMA-QZSI isolator are discussed. Finally, the static and dynamic experiments of SMA-QZSI are conducted to verify its force–displacement relationship and isolation performance. The results show that the proposed SMA-QZSI has remarkable low-frequency vibration isolation performance.

Syndiotactic chiral metastructure with local resonance for low-frequency vibration isolation

Isolating low-frequency vibrations is a challenge in engineering due to their long wavelength. The bandgap within inertial amplification metastructures has proven to be an effective solution for isolating low-frequency vibrations. In this study, a chiral local resonator is proposed and integrated into a syndiotactic chiral inertial amplification metastructure (SCM) to create a low-frequency bandgap. Under equal mass and stiffness conditions, SCM-CR exhibits a bandgap starting frequency 32.3 % lower than that of traditional metastructures with traditional local resonators (TM-TR), and the normalized width of the bandgap is 31.7 % wider than TM-TR. The low-frequency bandgap is attributed to the presence of chiral local resonators. The inertial amplification effect induced by the chiral structure results in a resonance frequency lower than that of local resonators with equivalent mass and stiffness. Within the low-frequency bandgap, the transmission of the SCM-CR proposed in this study exhibits double attenuation notches over a specific number of periods, leading to the normalized width of the deep attenuation region 45.8 % broader than that of traditional metastructures with chiral local resonators (TM-CR). The tunability of the bandgap has also been investigated. Experimental results verified the double attenuation notches and the tunability of the bandgap. This work provides a promising solution for low-frequency vibration isolation.

Topology optimization of programable quasi-zero-stiffness metastructures for low-frequency vibration isolation

Quasi-zero-stiffness (QZS) isolators have been demonstrated to realize low-frequency vibration isolation without loss of static stiffness. However, most previous designs are based on spring-driven links, cam-roller structures, or two-phased network structures resorting to complex assembling components, other than compact and integrative single-phased solid structures. In this paper, we propose a topology optimization scheme to inversely design QZS metastructures with smooth boundaries for customized nonlinear force-displacement curves. The optimization model is established based on the distinguishing features of the QZS force-displacement curve. The boundary smoothing procedure is introduced in the genetic algorithm to improve the convergence and stability of topology optimization. The designed metastructures are verified to have robust QZS feature. A linear relationship between the platform force and the initial modulus of the base material is obtained. We numerically show the high-static-low-dynamic performance, the load bearing, and even full band vibration isolation capabilities of the designed QZS metastructures. In addition, experiments are performed to verify the QZS feature of the designed metastructure. The inverse design scheme developed in this paper can efficiently design QZS isolators suitable for different scenarios with great flexibility. The metastructures with smooth boundaries are obtained so that postprocessing is not required before manufacture. The proposed inverse-design methodology paves the way for low-frequency vibration isolation using compact solid structures without any positive or negative stiffness units.

Novel Phononic-Like Crystal Wave Barrier Structure for Vibration Isolation

As an efficient, environmentally friendly, and economical urban public transportation tool, the subway has significant advantages compared to other urban public transportation tools and plays an irreplaceable role in the urban rail transit system. While the subway brings many conveniences to people, its operation has also brought a series of problems to urban development and residents’ lives, especially the vibration and noise problems generated by the subway have become unavoidable and urgent problems to be solved. The traditional wave barriers have a certain effect on attenuating and suppressing the vibration generated by the subway, but it has shortcomings in terms of the width and quantity of elastic wave bandgap (BG), so its application in low-frequency vibration reduction and isolation of subway systems is greatly limited. In order to broaden the elastic BG width and quantity of the wave barrier, this paper designs a novel phononic-like crystal subway wave barrier (PLCSWB) for subway vibration isolation based on locally resonant theory. Firstly, the dispersion curves of the novel PLCSWB are calculated using the improved plane wave expansion method and finite element method (FEM), and compared with the dispersion curves of traditional phononic crystal (PC) wave barriers. Secondly, the frequency response function of the novel PLCSWB is calculated using FEM to evaluate its attenuation effect on vibration, and the energy distribution characteristics at its BG boundary are analyzed. Then, the main factors affecting the BG of the novel PLCSWB are analyzed, and a spring–mass system equivalent model of the novel PLCSWB is established to theoretically estimate its BG range. Finally, the vibration data of the tunnel wall monitored on site are used to analyze and verify the vibration isolation effect of the novel PLCSWB. The results show that the novel PLCSWB opens five low-frequency BGs in the 200[Formula: see text]Hz frequency band, which increased the total width of the opened BGs by 49% compared to traditional PC wave barriers. In the frequency range of the BG, the attenuation value of the novel PLCSWB to vibration is mostly above 30[Formula: see text]dB, and the energy distribution inside the structure is mainly concentrated in the primitive cell that controls the BG, indicating good attenuation and control effects on vibration. The main factors affecting the BG of the novel PLCSWB are the density of the scatterer material, the elastic modulus, and the thickness of the wrapping layer material. Moreover, during subway operation, the novel PLCSWB has a good attenuation effect on the vibration transmitted from the tunnel wall to the soil. Among them, the maximum vibration acceleration amplitude of the novel PLCSWB with nine rows is reduced by 47%, and the vibration isolation performance is remarkable. The relevant research results of this paper provide a novel approach and method for the study of subway vibration reduction and isolation, and can also provide specific references for the design and development of wave barriers.