Low-frequency Vibration Isolation Research Articles

A novel method to solve the existed paradox of low-frequency vibration isolation and displacement attenuation in a nonlinear floating-slab on the wheel-rail loads

As we have known that it is impossible to attenuate the vibration displacement of the floating-slab depending on a strong stiffness and to improve the low-frequency vibration isolation performance of the floating-slab track (FST) depending on a soft stiffness simultaneously in engineering. In this paper, we propose a novel method to solve the paradox by introducing a “Hardening-First-Then-Softening” (HFTS) design based upon the energy distribution of wheel-rail loads to formulate a model of nonlinear floating-slab isolator. The average procedure is employed to analyze the vibration isolation ability of the isolator with parameters taken from a metro line load excitation. A simulation model of train-FST-tunnel with HFTS isolator is constructed to study the dynamic behaviors of the system. The numerical simulations show the significant suppression of displacement response of floating-slab and Z weighted acceleration vibration level of the tunnel. The results presented herein this paper provide a scheme to solve the strict requirements of displacement suppression and the vibration isolation which is of beneficial to steady and silent urban rail transit.

Bandgap and vibration isolation properties of cylindrical metastructure with chiral ring oscillators

A cylindrical metastructure with chiral ring oscillators is proposed for broadband vibration isolation, and experimental studies are carried out. The vibration transmission characteristics of cylindrical chiral metastructure is calculated and analyzed. Vibration transmission of three prototypes of cylindrical chiral metastructure is tested, and the results by using numerical simulation method are validated by the experimental results. It can be found that the broad bandgap can be created by the coupling bandgap between the multiple locally resonant bandgaps and Bragg scattering bandgap. Therefore, the good low-frequency vibration isolation performance can be achieved by designing the suitable parameters of chiral ring oscillators.

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.

A metamaterial sandwich plate with spring-lever-mass resonators

Sandwich plates are widely used in practical engineering, including civil engineering, transportation, aerospace, and other industrial fields. However, characteristics of high specific stiffness and strength cause poor performance in the vibro-acoustic fields. Therefore, resonators are introduced into the core of sandwich plates to improve their performance on vibration isolation. This paper proposes a new metamaterial sandwich plate, multiple spring-lever-mass resonators are introduced into the sandwich plate to obtain the low-frequency band gaps. The band structure of the metamaterial sandwich plate with spring-lever-mass resonators is calculated by the finite element method with the Bloch-Floquet theorem, and the band gap of the unit cell is obtained. The transmission spectra of the proposed structure are investigated to verify the accuracy of prediction results. The results show that effective performance on low-frequency vibration isolation via the metamaterial sandwich plate with spring-lever-mass resonators can be achieved, and this study can provide valuable references for related research and potential applications on the manipulation of wave propagation.

A Low-Frequency Vibration Isolator with Cross-Ring Structure

Low-frequency vibration isolation is essential for ultra-precision manufacturing and measurement equipment. Low stiffness is beneficial for low-frequency isolation, while leading to a degradation of the load capacity of the isolator. To tackle the problem, a nonlinear isolator is proposed with a cross-ring structure, composed of a circular ring and a semi-circular ring. Experimental studies validate that the isolator is applicable to different payload mass, and a cut-off frequency of 1.1[Formula: see text]Hz is achieved for an effective isolation. The isolator is theoretically investigated to reveal the mechanism leading to the low-frequency isolation performance. An elliptic integral method is adopted to characterize the stiffness characteristics of the ring structures under compression. The whole compression process of a semi-circular ring is divided into five stages according to the deformed shapes, exhibiting quasi-linear stiffness, stiffness-softening, negative stiffness, and stiffness-hardening characteristics in sequence. Together with the stiffness-softening circular ring, the cross-ring structure demonstrates a growing high-static-low-dynamic-stiffness (HSLDS) characteristic in a wide load range, and the result is verified by a restoring force measurement test. A harmonic balance analysis is performed to predict the frequency responses of the proposed isolator. It is shown that a low-frequency isolation can be achieved with the structure compressed to the HSLDS region by the payload, and an ultra-low-frequency isolation is achieved with the dynamic-to-static stiffness ratio below 0.1. A numerical investigation is performed to further reveal the frequency responses of the isolator with lightweight/overweight payloads and excessive excitation amplitudes. Jump phenomena are presented. This work provides a prototype and the theoretical basis for low-frequency vibration isolation via a cross-ring structure.

A creative wide-frequency and large-amplitude vibration isolator design method based on magnetic negative stiffness and displacement amplification mechanism

Negative stiffness vibration isolation devices have attracted significant attention and research interest for their ability to enhance the low-frequency vibration isolation performance of passive vibration isolators. However, their narrow linear negative stiffness region has hindered their broader application. To address this limitation, a novel design method for vibration isolators is proposed, integrating the permanent magnetic negative stiffness device (NSD) with the displacement amplification mechanism (DAM). The paper begins by presenting a specific vibration isolator design method and analyzing the kinematic relationship. Next, a single-degree-of-freedom (SDOF) nonlinear equivalent model of the vibration isolator is established using the pseudo-rigid-body model (PRBM) approach. Numerical simulations are then conducted to obtain the transmissibility of the isolator. Furthermore, two isolators—one with the displacement amplification effect and another without—are manufactured, and experimental investigations are carried out. The experimental results confirm that the incorporation of the displacement amplification mechanism effectively expands the linear negative stiffness region of the negative stiffness magnet pair, enabling wide-frequency and large-amplitude vibration isolation. Notably, these experimental findings align well with the simulation results. In summary, this paper proposes a creative design method for wide frequency and large amplitude vibration isolators, and proves it through theoretical analysis and experimental validation.

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

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

A novel bio-inspired kangaroo leg structure for low-frequency vibration isolation

A novel bio-inspired kangaroo leg structure for low-frequency vibration isolation

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

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

Bandgap regulations of longitudinal wave for a nonlinear metastructure isolator with high-static-low-dynamic stiffness

Linear structures are inherently difficult to exhibit mechanical properties with high-static-low-dynamic stiffness (HSLDS), which means that linear isolators with these structures struggle to have both high-quality load-bearing capacity and low-frequency isolation ability at the same time. To address this issue, we have designed a high-load-capacity local resonance (LR) nonlinear metastructure isolator for low-frequency vibration isolation of target objects. We reveal the regulation mechanism of longitudinal wave attenuation in such metastructures and conduct comparative study by finite element method (FEM) and experiments for a 3D printed prototype metastructure. The results show that in specific excitation frequencies, the LR nonlinear metastructure with a cantilever beam oscillator having a natural frequency of 11.7 Hz triggers a LR mechanism. Under the action of the nonlinear isolator, the vibration transmissibility is as low as 10 % at the center frequency of the bandgap under the base excitation. Furthermore, the dispersion equation of such nonlinear metastructures is derived, and through the analysis of the regulation of bandgaps, the variation trend of the transmissibility of nonlinear metastructure isolators is effectively predicted. The calculation method and design idea of this metastructure isolators provide a new approach for vibration isolation.

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

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

Vibration characteristics of additive manufactured IWP-type TPMS lattice structures

Several research has been done on the conventional strut-based lattice structures, which have the problem of stress concentration in the application. In recent years, a new lattice structure, the triply periodic minimal surface (TPMS) lattice structure is increasingly gaining attention, but its vibrational properties have been less studied. In this study, the IWP-type TPMS lattice structures and ordinary body-centered cubic (BCC) counterparts with similar topology were prepared by selective laser melting (SLM) additive manufacturing (AM) technique. The compression behavior of the structures and the energy absorption capacity were determined by uniaxial compression tests. The frequency response and the damping ratio of the structure were calculated by dynamic vibration transfer rate tests. The results show that the stiffness and inherent frequency of the lattice structure are proportional to the volume fraction and inversely proportional to the cell size. Decreasing the volume fraction and increasing the cell size can be more beneficial to achieve low-frequency vibration isolation. Moreover, the IWP-type triply periodic minimal surface lattice structures have better mechanical properties than BCC structures and have good vibration isolation properties. Insights from this paper provide a reference for improving the load-carrying and vibration isolation performance of lightweight lattice structures.

Bio-inspired multi-joint-collaborative vibration isolation

Inspired by the collaborative action of ankle, knee and hip joint, a novel bio-inspired multi joint structure (BIMJS) is proposed, and its favorable nonlinearity is systematically investigated for low frequency vibration isolation. Two rigid rods are adopted to imitate the femur and tibia, and three torsional springs are utilized to simulate the muscle function in each joint. Based on the principle of virtual work, a static model considering the action of three joints and leg posture is established to characterize the stiffness property. The independent action mechanism of each joint is revealed and the influence of posture adjustment on equivalent stiffness of the BIMJS is studied. By adjusting proper posture and setting reasonable stiffness of each joint, the quasi zero stiffness (QZS) can be easily obtained for low frequency vibration isolation. Dynamic model is developed and the displacement transmissibility is derived to estimate the isolation performance of the BIMJS. The experimental results confirm the advantages of realizing QZS and low-frequency vibration isolation under multiple loads. The vibrations above 2.5 Hz can be effectively isolated. The concept of utilizing the collaborative action of multi joints may provide an innovative method for the design of low frequency vibration isolators.

Load-adaptive quasi-zero stiffness vibration isolation via dual electromagnetic stiffness regulation

Conventional quasi-zero stiffness (QZS) isolators are sensitive to load variation, especially the load mismatch can severely degrade low-frequency vibration isolation performance. Herein, a load-adaptative electromagnetic QZS vibration isolator (LEQVI) is proposed. The stiffness nonlinearization for QZS characteristic is achieved by exploiting a nonlinear positive stiffness structure (a cylindrical coil and a magnet in the face-to-face configuration) to modulate a negative stiffness structure (a conical coil and a magnet in the nested configuration). Static modeling and tests reveal that the rated load of the LEQVI can be flexibly and linearly adjusted by regulating the excitation current. Dynamic modeling found that the load mismatch can narrow the vibration isolation bandwidth and deteriorate the vibration attenuation effect. A sliding mode control law considering input saturation is developed to adapt to unknown loads. Simulations and dynamic experiments are conducted to evaluate the vibration isolation performance and verify the effectiveness of the load-adaptive controller. The results demonstrate that the LEQVI can realize a wide vibration isolation band and effective vibration attenuation under various loads via dual electromagnetic stiffness regulation. The proposed LEQVI provides a novel perspective for designing load-insensitive QZS isolators and holds great promise in facilitating future engineering applications of QZS isolators.

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.

A tunable metamaterial using a single beam element with quasi-zero-stiffness characteristics for low-frequency vibration isolation

Quasi-zero-stiffness (QZS) isolators exhibit high-static and low-dynamic stiffness without sacrificing the load-bearing capacity and with the ability to shield the vibration in low-frequency ranges. Most of the current designs possess QZS property using a combination of positive stiffness element with negative stiffness element, increasing the complexity of the model. In the present research, a single-element mechanical metamaterial is tailored to obtain the QZS property. The building block consists of a single elastically-deformed beam, and the static results of the 3D-printed metastructure demonstrate QZS behavior. A mathematical model is developed for studying the nonlinear behavior of the proposed model, and the dynamic equation is solved using Harmonic-Balance method. Further, an experiment is performed to confirm the vibration isolation capability of the proposed model in low-frequency ranges. Stability analysis is performed mathematically using the perturbation analysis. The QZS mechanism obtained here solely depends on the flexible beam’s geometrical configuration, hence making the design strategy material independent.

Origami-inspired quasi-zero stiffness metamaterials for low-frequency multi-direction vibration isolation

Multi-directional low-frequency vibration isolation is an unavoidable problem in many practical engineering scenarios. However, to date, most works are unable to achieve this goal, and those that can do so only to some degree, but their structure is complex and large, limiting the range of applications in practical engineering. Here, we propose a kind of quasi-zero stiffness (QZS) metamaterial constructed from a series of Kresling-pattern origami-inspired structures, whose simple topology with reasonable design parameters can obtain the expected QZS features. Moreover, the decoupling strategy adopted by the proposed QZS metamaterials allows for the independent motion of adjacent unit cells, resulting in an improvement in controllability and programmability. We demonstrate, both in simulations and experiments, the design process and the multi-directional low-frequency vibration isolation characteristics of the proposed QZS metamaterial. This study provides a method for realizing multi-directional low-frequency vibration isolation, expanding the application potential of QZS metamaterials for broader needs.

Vibration isolator using graded reinforced double-leaf acoustic black holes - theory and experiment

The acoustic black hole (ABH) has aroused great interest and shown high potential of application in broadband vibration control using a lightweight structure. Yet conventional ABHs still suffer from intrinsic weak structural stiffness and poor broadband low-frequency performance. Besides, there is a lack of effective computational methods for the design of complex or composite ABH structures with practically required properties. In this paper, the vibration isolation of a beam with embedded graded reinforced double-leaf ABH (GRD-ABH) structures is investigated, focusing on improving both broadband low-frequency vibration isolation performance and the structural stiffness. The multibody system transfer matrix method (MSTMM) is proposed to model and simulate the compound ABH beam, which is treated as a multibody system with complex topology. Both the free and forced vibration analysis of the GRD-ABH are conducted and the results are compared with the finite element method (FEM), thus validating the correctness and high computation efficiency of the MSTMM. The results show that the GRD-ABH beam can simultaneously enhance a broadband low-frequency vibration isolation effect and the structural stiffness compared with the conventional periodic reinforced double-leaf ABH beam. The experiment further verified the correctness of the MSTMM and the effectiveness of the vibration isolation effect of the proposed GRD-ABH beam. The proposed theoretical approach and the graded reinforced double-leaf design provide the basis for solving the vibration isolation problem of more complex ABH structures.

Modeling and analysis of the magnetic force and stiffness of a low-frequency vibration isolator with axial magnetized magnetic rings.

The vibration isolator is a key part of many ultra-precision machines and measuring apparatus. Magnetic suspension vibration isolators (MSVIs) will have excellent application prospects in these instruments to restrain external oscillations. So this paper firstly proposes a new basic configuration of MSVI. Then, in order to study the mechanical characteristics of the MSVI, an analytical expression of the magnetic force is established. The effectiveness of which is demonstrated by the experiment and finite element analysis (FEA). The stiffness of the MSVI is obtained by the derivative of the established analytical magnetic force. Both the axial magnetic force and stiffness appear strong nonlinearity when the inner ring moves at both ends of the fixed outer ring. While the inner ring travels in the middle of the fixed outer one, the axial magnetic force and stiffness indicate approximate linearity with enough bearing capacity. Furthermore, parametric analysis, based on the created magnetic force and stiffness, is performed. The analytical results show that the axial magnetic stiffness may achieve a zero or even negative stiffness value in this range at some size dimensions. The MSVI appears to have a negative stiffness characteristic. More importantly, if a linear and nonlinear positive stiffness spring is combined with the MSVI, it can increase the load capacity of the MSVI. As an example study, the vibration isolation performance of the MSVI is analyzed. The vibration isolation calculation and experiment with the zero stiffness MSVI will be the further focus of the paper.

Low-frequency vibration isolation via an elastic origami-inspired structure

This paper presents a new elastic origami-inspired structure with quasi-zero-stiffness (QZS) characteristics to provide effective low-frequency vibration isolation performance. The geometric structure of the origami mechanism is first introduced, followed by the establishment of its mechanical model through the integration of elastic joints with compression springs. The derived strong nonlinear stiffness characteristics of the elastic origami mechanism are conducive to exploring a QZS isolator with high performance. Then by using the multiscale method, the dynamic behavior of the origami-inspired isolator is obtained, and the parameter influencing investigations validate that the proposed vibration isolation system has strong design flexibility and superior vibration suppression capability. An experimental prototype was fabricated and a series of vibration testing experiments under different working conditions were carried out. The experimental results demonstrated the effectiveness of the established theoretical model. Furthermore, the comparison with typical nonlinear passive isolators verified the advantages of the developed origami-inspired vibration isolation system. This work has the potential to advance the practical applications of origami-based mechanisms and also provides a new technical candidate for high-performance vibration isolation systems.