Nonlinear Vibration Isolation Research Articles

Chaotic band-gap modulation mechanism for nonlinear vibration isolation systems based on time-delay feedback control

Abstract Systems designed for nonlinear vibration isolation that incorporate chaotic states demonstrate superior capabilities in vibration attenuation, adeptly modulating the spectral constituents of vibrational noise. Yet, the challenge of eliciting low-amplitude chaotic dynamics and perpetuating these states across a diverse array of parameters remains formidable. This study proposes a pioneering strategy and technique for modulating the chaos band by incorporating a time-delayed feedback control mechanism within the framework of nonlinear vibration isolation systems.The investigation commences with an exhaustive analysis of the nonlinear dynamics, shedding light on the principles dictating the evolution of chaos. The study then advances to scrutinize the dynamics of systems with delays to elucidate the chaos-inducing processes engendered by feedback with temporal lags. Building upon the system’s responses, the chaotic performance and the effectiveness of the vibration isolation are crafted. Consequently, the time-delayed feedback control parameters are identified as pivotal design variables, which are then employed to dissect the control mechanisms influenced by the time-delayed feedback on the chaos band. Utilizing the delineated control mechanism, the nonlinear vibration isolation system is precipitously transitioned from a state of stable periodicity to one of chaos, fostering low-amplitude chaotic dynamics across an expansive parameter space, and in turn, resolving the previously stated challenge. Perhaps most significantly, the mechanism for attaining low-amplitude chaos introduced here paves the way for innovative methodologies in the active vibration isolation design of similar systems. Furthermore, it is anticipated to yield theoretical guidance for the manipulation of chaos bands and the formulation of active vibration isolation strategies within the domain of nonlinear vibration isolation systems.

Experimentally validated passive nonlinear capacitor in piezoelectric vibration applications

Abstract Piezoelectric vibration isolation and energy harvesting applications have been extensively studied in the literature. The studies include linear and nonlinear approaches. Linear methods are simpler but possess inherent limitations. On the other hand, nonlinear ones could perform better over a broader operating frequency range. Nonlinearity can be introduced in the mechanical domain or electrical domain actively or passively. Since electrical components can be on smaller scales compared to mechanical counterparts, inducing nonlinearity on the mechanical system through the electrical domain can be more practical. Moreover, passive structures require no energy supply and controller therefore they are simpler and more reliable than active ones. In this paper, a novel way to attain passive hardening stiffness was suggested by introducing an electrical component in a shunt circuit for passive nonlinear piezoelectric vibration isolation or energy harvesting applications and the induced structural non-linearity is demonstrated experimentally. A passive nonlinear component is suggested to be a hardening capacitor obtained by the P–N junction. An analytic model is derived for parallel connected macro-fiber composite (MFC) piezoelectric material attached bimorph configuration on a cantilever beam and the model is solved numerically. MFC integrated bimorph model, and P–N junction approximate model are presented. The frequency response of the coupled system is obtained by using numerical models and experiments. Both numerical analysis and experiments validated the hardening stiffness effect of the P–N junction. To the best of the authors’ knowledge, this study is the first study to demonstrate that nonlinear capacitance of P–N junctions can be used to attain nonlinearity in a mechanical system.

A nonlinear vibration isolator with an essentially nonlinear converter

This paper introduces nonlinearity into bilinear springs and proposes an efficient asymmetrical nonlinear frequency converter (NC) that has a non-reciprocal transmission, which cascades a nonlinear spring and a rope. To solve the vibration equations of both NC and the conventional NES, the Runge-Kutta method is utilized. A comparison is conducted between the amplitude attenuation rates of the NC and the conventional NES. The rate of energy dissipation is indicated by analyzing the remaining energy. According to numerical analysis results, NC has a better performance in suppressing vibration than the conventional NES within a certain range. The energy dissipation rate is higher under a wide initial condition. In addition, NC can cause energy to shift from low-frequency regions to high-frequency regions with wide frequency bands. NC has a broader frequency range and a wider range of applications. This research offers a new approach and strategy for exploring effective devices for damping vibrations.

Dynamic characteristics of nonlinear vibration isolator for gas turbine

AbstractIn this study, a theoretical model of the vibration isolation system of the gas turbine is developed and numerically solved. A simplified finite element (FE) model was also established to determine the response under the shock load. The results of the FE model are used to verify the effectiveness of the theoretical model and the numerical solution. The influence of isolator stiffness, vibration isolator damping, and vibration isolator nonlinear stiffness coefficient on the shock response of the vibration isolation system is studied using the controlled‐variable method. These parameters (stiffness, damping, and nonlinear coefficient) enter into the shock resistance design of gas turbine vibration isolators.

An adjustable stiffness vibration isolator implemented by a semicircular ring

Nonlinear vibration isolators with quasi-zero-stiffness characteristics offer broadband vibration isolations, while passive quasi-zero-stiffness isolators are unable to adapt to variable working conditions. To address the issue, a nonlinear semi-active vibration isolator based on a semicircular ring structure is proposed. As an elastic component, the semicircular ring exhibits nonlinear stiffness under a vertical compression at the centre. With a semi-active control of the horizontal distance between the two ends of the semicircular ring, a pre-deformed state is induced, and the stiffness characteristics are adjusted accordingly. A chained beam-constraint model is adopted to characterize the pre-deformed process and the vertical compression process, respectively. The adjustable nonlinear restoring force is accurately calculated and adopted for vibration analysis. A harmonic balance method is used to analyze the frequency responses of the isolator under different working conditions. The semicircular ring exhibits softening stiffness under a vertical compression, and the quasi-zero-stiffness region can be effectively adjusted by the pre-deformed process. With the vertical compression reaching a threshold, negative stiffness is presented along with a snap-through phenomenon due to the bi-stability. With the semi-active pre-deformed, the isolator demonstrates different resonant frequencies and different risks in the occurrence of the snap-through during vibration. To avoid the snap-through-induced impact, the control threshold of the pre-deformed is determined, depending on the payload mass, the excitation amplitude, and the damping coefficient. Experiments are performed to validate the adjustable stiffness and the frequency responses of the isolator, and both the jump phenomenon and the snap-through phenomenon are observed.

A ring metastructure vibration isolator with thin beams

Conventional linear vibration isolators are difficult to have the function of high load-bearing capacity and low-frequency isolation, however nonlinear metastructure vibration isolators can effectively achieve this function. In this study, a new ring metastructure vibration isolator with thin beams was designed to have high static and low dynamic stiffnesses. We have accurately derived the static expression of these thin beams, obtained the stiffness characteristic and innovatively analyzed the vibration transmission characteristics of the ring isolator by deriving its dispersion equation. The influences of damping, frequency ratio, mass ratio, stiffness ratio, linear stiffness and nonlinear stiffness on the wave vector were obtained using the dispersion equation. Finally, a ring metastructure isolator sample with the high load-bearing capacity was designed and fabricated, and a vibration experiment was conducted to verify that the isolator has a lower vibration transmissibility in the target frequency band. This study not only demonstrates the feasibility of applying thin beams to nonlinear metastructure isolator design from mathematics, but also reveals profoundly its physical connotation from structural dynamics.

Vibration isolation platform for large-amplitude-low-frequency excitation by parallel-stack-assembly design of Miura origamis

To achieve an ultralow-frequency vibration isolation platform for simulation of space environment, suspension method is always utilized. However, the natural frequency of the suspension system is inversely proportional to the length of the suspension cable. In order to further reduce the dynamic stiffness, compress the suspension area, and achieve vibration isolation for wide-amplitude excitations, we propose parallel-stack-assembly (PSA) design principle for Origamis to construct absolute zero-stiffness for required intervals. The dynamic model for wide-range amplitude and deformation, design criteria for required low-frequency large-amplitude isolation effectiveness, and analysis for nonlinear vibration isolation property are given. Finally, the prototype is carried out to validate the theoretical analysis and design principle. The PSA design principle of Origamis creates the large-amplitude and ultralow-frequency isolation property, and, the study expands the applicability of isolators for low-frequency excitation with large amplitude for the systems in aviation, marine etc.

An investigation of a self-powered low-frequency nonlinear vibration isolation system

High-static-low-dynamic stiffness vibration isolation are of utmost significance in low-frequency vibration isolation. However, their intricate mechanisms are always challenging for environmental vibration changes. In this study, a self-powered nonlinear vibration isolation system with two stages is studied, with the aiming of obtaining the broadband vibration isolation. Magnetic springs of negative stiffness combined with the coil could transform mechanical vibration into electrical energy in lower stage. The feedback electrical energy could power the piezoelectric actuator in the upper stage. Based on the governing equations measured in stable equilibrium, the harmonic balance analysis is used to derive the frequency response functions of the transmissibility and the output power in the mechatronic resonance. The frequency band of vibration isolation extends to the lower frequencies and two resonance peaks reduce to the lower levels. The numerical simulations results validate the analytical solutions. Then the shock isolation performance is illustrated under the round step displacement and rounded pulse displacement. The parameter study demonstrates numerically that introduction of the high-static-low-dynamic stiffness improves the shock isolation performance. Moreover, the lower stage mechanical energy could drive the piezoelectric stack, resulting in high-efficiency shock isolation. Finally, an experiment is employed to prove the high-efficiency vibration isolation.

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.

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.

Nonlinear behavior of quasi-zero stiffness nonlinear torsional vibration isolator

Nonlinear behavior of quasi-zero stiffness nonlinear torsional vibration isolator

Analytical study on nonlinear frequency response and vibration isolation of multistage clutch damper in automotive powertrain

This paper studies the nonlinear frequency response and vibration isolation performance of the multistage clutch damper at resonance. First, a 2-DOF drivetrain model is established considering the piecewise-linear stiffness, piecewise-linear damping and asymmetric transition angles of the multistage clutch damper. Then, the averaging method is employed to deduce the analytical solution of the nonlinear motion equation, and the stability of the periodic solution is studied using Routh-Hurwitz criterion. The nonlinear behaviors of the oscillator are discussed based on the theoretical results, and the numerical simulation is carried out to verify the credibility of the proposed method. Finally, the sensitivity analysis is conducted to investigate the influence of the system parameters on the amplitude-frequency response of the multistage clutch damper. The results indicate that the isolation performance of the multistage clutch damper is sensitive to the first and second stages of damping and the first-stage transition angles. By increasing the first and second stages of viscous damping by 50% and simultaneously reducing the first-stage angle range by 3° with 1° asymmetry, the isolation performance of the clutch damper is effectively improved, reducing the vibration amplitude at resonance by 28.8%.

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

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

Reliability-based design optimization scheme of isolation capacity of nonlinear vibration isolators

Nonlinear vibration isolators (NVIs) are beneficial to isolate or suppress the adverse effects caused by harmful vibration. To a large extent, the isolation capacity of NVIs depends on the selection of design parameters (including structural, geometric, and excitation parameters) of vibration isolators. However, existent uncertainties of these parameters are unavoidable, which influence the reliability of the isolation capacity of NVIs. In this respect, an effective reliability-based design optimization (RBDO) scheme of isolation capacity of NVIs is presented by taking into account the parameter uncertainties of NVIs. In the proposed RBDO scheme, the force transmissibility of nonlinear isolators is regarded as the objective function, and the fundamental frequency, the dynamic displacement response amplitude, and reliability of vibration isolation performance are supplied as the constraints to search the optimal design parameters of NVIs. Considering the influence degree of design parameters uncertainties, the global reliability sensitivity analysis is employed for identifying the critical design parameters in NVIs. A surrogate model of the failure probability function is established by the adaptive learning Kriging approach to decrease the computational cost of the reliability evaluation nested in the RBDO scheme. An advanced meta-heuristic algorithm is executed to search for the design parameters for optimal isolation capacity of NVIs. The proposed scheme provides a potential direction for optimizing the isolation capacity of complicated vibration isolators.

Numerical and experimental investigation of a high-static-low-dynamic stiffness vibration isolator with tunable stiffness and damping

Nonlinear vibration isolators that take advantage of negative stiffness elements can simultaneously meet the requirements of acceptable static deflection and frequency band of isolation and are thus superior to their linear counterparts. Incorporating electromagnetic elements into the vibration isolator is a common approach to provide the required negative stiffness. Electromagnetic mechanisms are low-cost, tuneable, and operate without friction. Also, they can extract or dampen the energy of the host system through electromechanical coupling. Therefore, electromechanical elements are ideal choices for designing multi-purpose vibration control mechanisms. In this study, three coils surrounded by arrays of permanent magnets are considered. When the system vibrates, their magnetic fields interact with that of a moving magnet attached to a rod supporting an isolated mass. The electromagnetic properties of the proposed system are simulated using the finite element method (FEM) and experimental measurements are used to validate the numerical simulations. Different scenarios for a system consisting of three coaxial coils are considered and compared, including powering the coils, open circuit coils, short circuit coils and coils shunted with an external circuit. Features of each case are discussed and general guidelines for designing a multipurpose vibration controller are given.

A study of a nonlinear vibration isolator supported on an imperfect boundary plate

The research on the nonlinear vibration isolation of continuum systems always focuses on the perfect boundary conditions. In this work, nonlinear isolation of transverse vibrations of the arbitrary boundary rectangular plate was investigated. A novel analytical approach was proposed. The rigid body dynamics and high-order energy Fourier series expansion method were utilized to establish a mathematical model of the arbitrary boundary nonlinear continuum system. This method involves the simultaneous Fourier series expansion in temporal and spatial domains. The dynamic behaviors of an arbitrary boundary rectangular plate with nonlinear vibration isolators can be described through a harmonic balance analysis together with arc-length continuation. The convergence and stability for the frequency response functions were checked via the Lyapunov stability theory. The numerical results supported the analytical solutions. Both the analytical and numerical results demonstrated that nonlinear broadband vibration isolation is sensitive to the elasticity of the arbitrary boundary flexible foundation. Furthermore, increasing damping can effectively suppress the transmission of low-order vibrations and control the divergence of higher-order vibrations. Finally, an experiment rig was designed to validate the nonlinear isolation of the transverse vibrations of an arbitrary boundary plate.

Parametric study of the axial force and negative stiffness of an electromagnetic mechanism for vibration isolation applications

Nonlinear vibration isolators that take advantage of negative stiffness elements can provide high static stiffness to bear high static loads and quasi-zero dynamic stiffness to widen the isolation frequency band and hence are desirable for vibration isolation. Electromagnetic negative stiffness elements can be used to design and fabricate quasi-zero-stiffness vibration isolators. Different combinations of permanent magnets and electromagnetic coils in attractive or repulsive configurations can lead to negative stiffness. The magnitude of the electromagnetic restoring force and negative stiffness is dependent upon many geometric and electromagnetic parameters and is controllable by adjusting the current in the electromagnetic coils. The present work compares the negative stiffness properties of three different configurations and provides a general guideline for selecting the appropriate configuration. The finite element method is used to simulate the magnetic fields and electromagnetic force acting on the permanent magnet. Numerical results are presented, and findings are validated by analytical solutions.

Nonlinear Vibration Isolation of Spacecraft System by a Bionic Variable-Stiffness Device Enhanced by Electromagnetic Component

Nonlinear Vibration Isolation of Spacecraft System by a Bionic Variable-Stiffness Device Enhanced by Electromagnetic Component

Design and correlation analysis of quasi-zero stiffness passive vibration isolation air spring

Vibration isolation systems are widely used in high-end automobile manufacturing, precision instrument processing, building and bridge seismic resistance, ship machinery noise reduction and other engineering fields, with good development prospects. At present, the existing vibration isolation systems on the market are mainly divided into active and passive vibration isolation systems. Passive vibration isolation does not require external energy input. Its structure is simple and the control scheme is easy to implement. However, passive vibration isolation performs well in high frequency vibration but not in low frequency. As a new nonlinear low-frequency vibration isolation technology, the quasi-zero stiffness vibration isolation system has changed the traditional concept of linear system vibration isolation. In addition, compared with traditional spring, air spring as a new type of elastic vibration isolation mechanism has many excellent performances, such as high fatigue resistance and high stiffness. Therefore, this paper uses air spring to design a passive vibration isolation quasi-zero stiffness air spring structure with good vibration isolation effect, simple structure and low cost in both low-frequency and high-frequency vibration.

Analysis on nonlinear stiffness isolators revealing damping thresholds

Nonlinear vibration isolators with stiffness nonlinearity show promise for a broadband isolation performance without degrading the load capacity. An analytical method is proposed to predict all the possible frequency responses of nonlinear stiffness isolators under different damping. The vibration equation is transformed into an algebraic equation through harmonic balance method. The equation is regarded as a function of the frequency instead of the amplitude, leading to a general analytical method with its complexity independent with the order of the nonlinear stiffness. A damping threshold function is proposed based on the root conditions of the frequency, and the whole damping region is divided into large damping, medium damping and small damping sub-regions accordingly. The root conditions and the frequency responses in each sub-region are analytically analyzed. All the possible responses are classified into five categories based on the damping thresholds and the existence of a jump phenomenon. Nonlinear phenomena of full-band isolation, bounded response and unbounded response are revealed according to multivalued roots of the frequency, and their sufficient and necessary conditions are presented. Simulations are performed on nonlinear isolators with cubic stiffness, high-order stiffness, and non-polynomial stiffness, respectively. The damping thresholds, frequency response categories, and the nonlinear characteristics of each category are demonstrated for the studied cases. A high-order harmonic balance method and the Runge–Kutta method are adopted to verify the effectiveness of the proposed method. This work presents a general analytical method for the prediction of frequency responses, the determination of damping thresholds, and the theoretical illustrations of unique behaviors for nonlinear stiffness isolators.