Vibration Isolation Research Articles

The vibration isolation and sound radiation reduction characteristic of the micro-floating raft array skin

The vibration isolation and sound radiation reduction characteristic of the micro-floating raft array skin

Nonlinear effect on stable state and snap-through bistability of square composite laminate

Bistable structures with the elastic instability caused by buckling are confirmed to perform significantly in micro-electromechanical systems, metamaterials, energy harvester, vibration isolation and morphing structures. The target of this paper is to explore the dynamic responses of cross-ply bistable composite laminate, focusing on the nonlinear effect of the single- and double-well vibration. Both theoretical and finite element (FE) methods are employed to simulate the nonlinear vibration and dynamic snap-through of bistable composite laminate under the foundation excitation at the center. In the theoretical model, the governing equations are established via Lagrange's equation based on the first-order shear deformation theory, von Karman nonlinear strain-displacement relation and Rayleigh-Ritz method. The fourth-order Runge-Kutta method is adopted to solve the governing equations, and the numerical results are validated by FE model. Subsequently, the details of the dynamic responses are analyzed to identify the nonlinear effects in the form of bifurcation diagram, phase portrait, time history, Poincare maps and amplitude spectrum. The dynamic responses are examined for a series of excitation parameters in both time and frequency domain. Through fixed frequency and frequency sweep tests, the nonlinear phenomenon of the single- and double-well vibrations are analyzed including superharmonic resonance, stiffness softening, hysteresis phenomenon, various periodic and chaotic vibration. The diverse responses to external inputs contribute significantly to efficiently predicting mechanical behaviors in real-world conditions, thereby offering indispensable theoretical support for structural design applications.

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.

Geometric Parameter Effects on Bandgap Characteristics of Periodic Pile Barriers in Passive Vibration Isolation

To investigate the impact of the geometric parameters of periodic pile barriers on bandgap characteristics in passive vibration isolation, a two-dimensional, three-component unit cell was developed using the finite element method (FEM). This study analyzed the bandgap properties of periodic pile barriers and validated the effectiveness of the FEM through model testing. The FEM was then methodically applied to evaluate the effects of pipe pile thickness, periodic constant, arrangement pattern, and cross-sectional shape on the bandgap characteristics, culminating in the proposition of a novel H-shaped cross-section for the piles. The results demonstrated that the FEM-calculated bandgap frequency range, featuring steel piles arranged in a square pattern, closely aligned with the attenuation zone in the model tests. The lower band frequency (LBF) was primarily influenced by the pipe pile’s inner radius, while the upper band frequency (UBF) was predominantly affected by its outer radius. As the periodic constant increased, the LBF, UBF, and the width of band gap (WBG) all decreased. Conversely, changing the arrangement pattern from square to hexagonal led to increases in UBF and WBG, while the LBF diminished. Notably, the WBG of the H-section steel piles, possessing the same cross-sectional area, was 1.31 times greater than that of the steel pipe piles, indicating an enhanced vibration isolation performance. Additionally, the impact of transverse and vertical characteristic dimensions of the H-shaped pile on the band gap distribution was assessed, revealing that the transverse characteristic dimensions exerted a more significant influence than the vertical dimensions.

A kind of single-phase full bandgaps phononic crystals and experimental evidence

The exceptional performance of locally resonant phononic crystals (PCs) in vibration attenuation and noise reduction within nuclear power plants has garnered widespread attention in scholarly circles. To address the need for improved predictive accuracy in substrate structures characterized by significant flexibility, a one-dimensional mechanical model rooted in the mass-spring chain paradigm has been established. This model offers a straightforward and accurate means of predicting the lower and upper frequencies of the initial bandgap within locally resonant phononic crystals. Moreover, the dynamic model elucidates modal characteristics and vibrational responses inherent to locally resonant phononic crystals. Utilizing the proposed model, a singular-phase phononic crystal structure boasting full bandgaps has been devised. This structure facilitates the omnidirectional acquisition of locally resonant bandgaps across an exceedingly low-frequency spectrum through the incorporation of cantilever beam elements. Such a design holds immense promise within the realm of large-scale mechanical vibration isolation. As a means of validation, steel samples embodying this phononic crystal model were fabricated. Experimental results demonstrated an insertion loss of approximately 18.67 dB, affirming the vibration isolation efficacy of the singular-phase phononic crystal configuration.

Compliant curved beam support with flexible stiffness modulation for near-zero frequency vibration isolation

Passive isolation of low-frequency vibrations poses a significant challenge due to the requirement of possessing a low stiffness. Herein, a compliant curved beam support (CCBS) for near-zero frequency vibration isolation is proposed and systematically investigated. The CCBS exploits nonlinear negative stiffness provided by an arc-shaped beam support to modulate nonlinear positive stiffness of a spiral-shaped beam support. This nonlinear configuration gives rise to an interesting phenomenon, that is, the stiffness modulation of the CCBS for quasi-zero stiffness (QZS) can be flexibly fulfilled by performing a translation transformation on negative stiffness instead of reshaping it. A thorough static analysis is implemented to reveal this stiffness modulation mechanism. The dynamic governing equation is derived and solved analytically and numerically to calculate the displacement transmissibility, and the effects of excitation amplitude, damping, and applied load are dissected. Finally, various excitation tests are conducted to experimentally evaluate vibration isolation performance. The results demonstrate that the CCBS exhibits a remarkably low resonance frequency of 0.5 Hz and achieves near-zero isolation starting at 0.8 Hz, showcasing excellent performance in isolating low-frequency vibrations. The proposed CCBS provides a novel paradigm for achieving flexible low stiffness modulation in compact QZS isolators, making it highly deserving of promotion.

Meta-arch structure: Designed reinforcement cage to enhance vibration isolation performance

In this study, inspired by the mechanical metamaterials with bandgap properties, a new type of meta-arch structure (MAS) for the attenuation of elastic waves is proposed. In this metastructure, the reinforcement cage, typically employed to enhance the tensile properties of building materials, has been redesigned and transformed into a new structure containing circular tubes with embedded resonant microstructures. The vibration reduction performance of the MAS was illustrated by the frequency response analysis in the simulation calculation, and the generation mechanism of the vibration attenuation band was revealed. The specimens of the complex MAS consisting of gypsum, reinforced steel bars, and tubes were fabricated, and the vibration response experiments were carried out to determine the dynamic properties of the novel MAS. The results show that the designed arch structure exhibits a broad vibration attenuation band without sacrificing its structural bearing capacity. Additionally, the robustness of the band gap is demonstrated by analyzing how changes in the positions of excitation and response points influence the band gap. Moreover, the MAS can be customized for specific application scenarios of vibration reduction according to the parameter analysis. Finally, the experimental results closely align with the numerical estimations, confirming the feasibility of the design method for reducing vibrations. This work provides a new method for the development of building structures for vibration and noise control.

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.

Enhancement of rider comfort by magnetorheological elastomer based damping treatment at strategic locations of an electric two wheeler

The vibrations generated in the two-wheeled vehicles like motorcycles due to road irregularities such as cracks, potholes, and bumps on the road cause discomfort for the rider as well as the pillion. These vibrations are reported to cause lower back pains, musculoskeletal effects, fatigue, and long-term health issues. Particularly, electric two-wheelers are more susceptible to these vibrations caused by the road and need attention. This paper presents an innovative technique for the reduction of vibrations at prominent locations in the electric two-wheeler to improve the rider’s comfort. All measured accelerations are about vertical direction (along z-axis as per ISO 2631-1 standard). Passive and Semi-active damping treatments namely, Room temperature vulcanizing Silicone rubber and Magnetorheological elastomer (MRE) were applied on the test vehicle at strategic locations of vibration. Both were compared for their effectiveness in reducing the vibrations. Results showed that MRE based damping technique proved better vibration isolation at the strategic locations. The weighted root mean square acceleration as well as vibration dose values were found to decrease with the help of damping treatments thus improving the rider’s overall comfort level.

Study on the effect of nonlinear inertia on the vibration isolation performance of quasi-zero-stiffness isolators

Typically, when subjected to excessive external force, quasi-zero-stiffness isolators with low damping will cause a sharp rightward bending of the transmissibility curve, resulting in a substantial decline in the performance of vibration isolation. The scheme with parallel tunable nonlinear inertia (PTNI) based on the triple-spring quasi-zero-stiffness (TS-QZS) isolator is designed to solve the above problems. To begin with, the kinetic equations are derived. Subsequently, the analysis of the primary response and stability involved the utilization of the Harmonic Balance Method (HBM), and the accuracy of the model was validated through numerical calculations. Finally, the impact of essential parameters is examined. The findings suggest that the QZS-PTNI isolator, without compromising the high frequency transmissibility, is capable of reducing peaks, suppressing the rightward trend of the transmissibility curve, narrowing the range of jump-up and jump-down frequency, and enhancing the vibration isolation performance.

A high-static-low-dynamic-stiffness delayed resonator vibration absorber

Delayed resonator (DR), which enables complete vibration suppression through loop delay tuning, has been extensively investigated as a linear active dynamic vibration absorber since its invention. Besides, the nonlinear high-static-low-dynamic stiffness (HSLDS) has been widely used in vibration isolators for broadband (yet incomplete) vibration reduction. This work combines the benefits of DR and the nonlinear HSLDS characteristics, thus creating a nonlinear DR (NDR). Three unexplored topics are considered: (1). To address the nonlinear dynamics that are made complicated by the introduction of delay and the nonlinearity coupled between the NDR and the primary structure; (2). To tune the control parameters to seek possible complete vibration suppression in the nonlinear case, and accordingly, to determine the operable frequency band; (3). To evaluate how the HSLDS characteristics can enhance the performance of the linear DR (LDR) and how to design an NDR to maximize its benefits. Without loss of generality, a classic nonlinear HSLDS structure with three springs and two links is considered, and mathematical tools and computational algorithms are introduced or proposed to efficiently address theoretical analysis. Using the parameters of an experimental setup, we show that a properly tuned NDR suppresses the vibrations on the primary structure to a sufficiently low level. Besides, the HSLDS characteristics extend the operable frequency band compared with the LDR, while strong nonlinearity limits such extension. The proposed analysis procedures for delay-coupled nonlinear dynamics, alongside the control parameter tuning, determination of operable frequency bands, and structural design rules, establish a basic theoretical framework for the NDR design.

Research on active-passive integrated vibration isolator based on metal rubber and piezoelectric actuator

Abstract The paper introduces a novel active-passive integrated vibration isolator based on metal rubber and piezoelectric actuator, along with an adaptive active vibration control strategy. The active control strategy employs the adaptive dynamic step filtered-x normalized least mean squares algorithm, allowing the step size to adaptively adjust with the error. The secondary control path of the algorithm is modeled using the enhanced rate-dependent Prandtl–Ishlinskii model and the auto-regressive with extra inputs model. The active-passive integrated vibration isolator achieves broadband vibration isolation from 10 to 200 Hz. Compared to passive isolation, the transmissibility decreases from 0.99 to 0.056 at 10 Hz, from 3.02 to 0.068 at the resonance frequency, and from 0.057 to 0.046 at 200 Hz. This study provides a theoretical and experimental foundation for the design of a novel, broadband, and efficient active-passive integrated vibration isolator structure and active control method.

Mechanical properties of a novel negative Poisson's ratio gradient structure

A novel cellular structure is proposed based on bionic structure with negative Poisson's ratio characteristic, and the cell is periodically expanded in the in-plane direction to create a new honeycomb structure. The influence of gradient changes of the structural parameters on the load-bearing capacity and damping characteristics of the structure is investigated through a combination method of finite element numerical simulations and experiments. The results indicate that the concentric gradient arrangement of cell wall thickness and angle parameters, and the symmetrical gradient arrangement of cell height, wall thickness and angle parameters have the most significant influence on the static bearing capacity of the structure. In contrast, the gradient arrangement under the corner circle diameter has minimal effect on the static bearing capacity of the structure. Under the same conditions, the peak values of the transmissibility of C2 (large angle at constraint end and loading end, and smaller angle in the middle) and C3 structures (angle gradually increases from the loading end to the constraint end) are significantly reduced between the frequency 2 Hz and 1024 Hz. The peak values of the transmissibility of the structures C2 and C3 are respectively decreased by 20% and 25% compared to that of the non-gradient structure. This shows that the vibration damping effect of these two structures is better. The structure with the gradient change and the structure without the gradient change of the new honeycomb structure can both achieve certain vibration reduction and isolation from the middle to high frequency range.

Bio-inspired vibration isolator with triboelectric nanogenerator for self-powered monitoring

Vibration isolators are used in many engineering projects, but their real-time monitoring and early warning still a challenge. This paper presents a novel bio-inspired vibration isolator with triboelectric nanogenerator (BVI-TENG), which can be applied on vibration isolation and structural health monitoring. To find the optimal combination of parameters to achieve quasi-zero stiffness, the relationships between the force–displacement and the stiffness-displacement are investigated. After establishing the dynamic model, the effects of the different parameters on the amplitude-frequency are explored by using the harmonic balanced method. To explore the vibration isolation performance, the force transmissibility is analyzed. It was found that BVI-TENG can isolate the low-frequency and even ultra-low frequency vibration. By setting up and testing the experimental prototype, the theoretical results are verified. The energy harvesting performance of BVI-TENG is investigated by analyzing the output current, output voltage and transfer charge under different frequency. By tuning the loading resistance, the maximum output power of BVI-TENG is found. More importantly, the structural health monitoring part of the BVI-TENG produces AC signal in the safe region, which can be harvested and stored, and the signal transforms immediately into DC signal when out from this region. The performances demonstrate that the BVI-TENG can be applied to vibration isolation and serves as a self-powered structural health monitoring device to meet the needs of the civil engineering, ocean platform, and industrial robot.

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.

An active-passive integrated actuator based on macro fiber composite for on-orbit micro-vibration isolation

Micro-vibration suppression is crucial for satellites to ensure high imaging performance of optical loads. Herein, an active-passive integrated actuator based on macro fiber composite for micro-vibration isolation is proposed and investigated. Integrated passive and active vibration suppression is achieved by arraying a composite laminated beam consisting of the stiffness layer, damping layer and macro fiber composite layer. A dominant-frequency-correction hysteresis modeling strategy is devised to describe the asymmetric and rate-dependent voltage-force hysteresis of the proposed actuator. By treating the correction as a disturbance, the voltage-force hysteresis is compensated in combination with an extended state observer. In order to achieve resonance suppression, a full-estimation-feedback controller featuring merely displacement response feedback is developed exploiting the estimation of the extended state observer as feedback. Simulation results verify that the full-estimation-feedback controller is capable of suppressing the resonance peak with weak adverse effects on the transmissibility in the isolation band. Finally, experiments are performed to identify the voltage-force hysteresis model and evaluate the vibration isolation performance. Periodic and sweep excitation test results demonstrate that in passive mode, the actuator has a small resonance frequency of 2.3 Hz and a wide isolation band starting from 3.5 Hz. With the full-estimation-feedback controller, the resonance peak is effectively suppressed using a single signal feedback, while maintaining excellent vibration attenuation within the isolation band. The proposed actuator provides a paradigm for the design of active-passive integration vibration isolators for broadband micro-vibration suppression, which holds significant promise in enhancing the effectiveness of current observation missions.

Broadband vibration isolation in cylindrical shells embedded with total reflection elastic meta-shells

In this research, we propose a pioneering conceptual design paradigm of elastic meta-shells for broadband elastic wave control in cylindrical shells. We theoretically reveal the mechanism for wave isolation in cylindrical shells, which arises from the closure of all transmission channels (i.e., total reflection) when 0th-order diffraction is the only remaining diffraction mode. In addition, to solve the dynamic coupling behavior between multi-order diffraction modes, we extend the acoustic mode-coupling theory to elastic waves in cylindrical shells. Based on the diffraction theory and multiple reflection effect, we construct a total reflection elastic meta-shell and numerically demonstrate efficient broadband elastic wave isolation in the frequency range of 5 k–7 kHz. Finally, the vibration isolation performance is experimentally verified by embedding a total reflection elastic meta-shell in a finite thin-walled cylindrical shell waveguide. Results confirm the feasibility of the elastic meta-shell design concept and its ability to achieve fully passive, high-efficiency, and broadband vibration isolation. Our vibration isolation strategy could broaden the applicable scope of elastic meta-structures and open new horizons for vibration isolation, mechanical energy filtering, and elastic wave signal processing in cylindrical shells.

Comprehensive analysis of a butterfly-shaped piezoelectric shunting vibration absorber for robust vibration reduction and isolation: Theoretical and experimental validation

The Piezoelectric Shunting Vibration Absorber (PSVA) has garnered attention for its effectiveness in vibration control. This paper aims to propose a novel PSVA capable of simultaneously amplitude reduction and vibration isolation under various conditions. The PSVA consists of a butterfly-shaped link component and a piezoelectric stack, connected to the structure to be damped via bolts. Subsequently, an equivalent schematic diagram of the PSVA is established, and its equivalent stiffness is determined. Taking a single-degree-of-freedom structure as an example, considering the dynamic stiffness of the shunting circuit, a dynamic model of the electromechanical coupled system is developed, obtaining the system’s acceleration response and force transmissibility frequency response functions. Following this, experimental equipment is designed and fabricated, and the performance of the PSVA is tested under various excitation conditions. Finally, inspired by the experimental results, a segmented inductance circuit is designed and tested for its capability to broaden the vibration control bandwidth.

A numerical approach to levitated superconductors and its application to a superconducting cylinder in a quadrupole field

Abstract Magnetically levitated superconductors in the Meissner state can be utilized as micro-mechanical oscillators with large mass, high quality factors and long coherence times. In previous works analytical solutions for the magnetic field distribution around a superconducting sphere in a quadrupole field have been found and used to derive the trap parameters, while non-spherical geometries have only been investigated in a few idealized cases. However, superconductors of almost arbitrary shape can be used as levitators in a magnetic trap and, as the trap’s properties depend strongly on the superconductor’s shape, allow for a wider parameter regime to be accessed. Finite element models are suitable to obtain the field distribution around arbitrarily shaped superconductors in arbitrary fields, but have not yet been used widely in the context of levitated superconductors. Here we present a simple numerical model for this purpose and use it to calculate the field distribution around cylindrical superconductors in a quadrupole field and to evaluate the trap parameters. We find that the cylindrical shape, compared to spherical levitators, allows for substantially higher trap frequencies and coupling strengths. This in turn reduces the demands on vibration isolation and significantly eases the requirements for feedback cooling to the ground state. The numerical model is provided in a file repository and can easily be adapted to various geometries and trap fields.

A semi-active adaptive pneumatic vibration isolator based on frequency response analysis and nonlinear control

In this work, an adaptive nonlinear error feedback controller based on fuzzy state observer is proposed to a novel rubber pneumatic vibration isolator (PVI) system. First, a novel rubber PVI system is designed and developed. Harmonic balance method is applied to establish the dynamic model of the PVI system, so as to analyze the frequency response characteristics of the system. Second, to improve the PVI performance in low-frequency vibration, a nonlinear state error feedback control system based on fuzzy state observer is designed for the active PVI system. Furthermore, the experiment system is established. Finally, through the experimental comparison under 5 Hz, 7 Hz, 20 Hz, and 40 Hz, an adaptive PVI strategy is proposed. The experimental results demonstrate that the adaptive PVI shows better performance in vibration isolation.