Isolation Frequency Band Research Articles

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.

Investigation of the vibration isolation effect of composite vibration isolation walls on ground surface vibrations in deep tunnels of suburban railways

To investigate the vibration isolation effect of composite vibration isolation walls on surface vibrations in suburban railway deep tunnels under various influencing factors, an integrated numerical model of the train was initially developed. This model solved the wheel-rail interaction force and was applied to a three-dimensional volume coupling model of the track soil. Subsequently, the model's reliability was validated through comparison with measured data. Afterward, the vibration isolation effects of various types of EPS material vibration isolation walls were examined, with a focus on exploring the impact of thickness, material proportion, and relative positioning of the materials within the vibration isolation wall composed of EPS material and concrete. Research indicates that with an increase in the burial depth of a single material vibration isolation wall, its effective vibration isolation frequency range gradually widens. When the burial depth of the vibration isolation wall exceeds the tunnel burial depth, the vibration isolation effect is optimal. Composite vibration isolation walls, with thicknesses smaller than single-material vibration isolation walls, exhibit superior vibration isolation effects compared to their single-material counterparts. The effective vibration isolation frequency band of composite vibration isolation walls differs from that of single-material vibration isolation walls. Using the optimal-size vibration isolation wall of a single material as a composite vibration isolation wall enhances the vibration isolation effect of peak acceleration in the frequency domain by 16.58% and peak velocity by 16.95%. Moreover, frequency domain peak displacement experiences a 30.73% improvement in the vibration isolation effect.

Design of low-frequency circular metastructure isolators with high-load-bearing capacity

Traditional vibration isolation structures cannot work effectively for low-frequency vibration under heavy loads, due to the inherent contradiction between the high-static and low-dynamic stiffness of these structures. Although the challenge can be effectively addressed by introducing a negative stiffness mechanism, the existing structures inevitably have complex configurations. Metastructures, a class of man-made structures with both extraordinary mechanical properties and simple configurations, provide a new insight for low-frequency vibration isolation technology. In this paper, circular metastructure isolators consisting of some simple beams are designed for low-frequency vibration, including a single-layer isolator and a double-layer isolator, and their static and dynamic characteristics are studied, respectively. For the static characteristic, the force–displacement and stiffness–displacement curves are obtained by finite element simulation; for the dynamic characteristic, the vibration transmissibility curves are obtained analytically and numerically. The result shows that the circular nonlinear single-layer isolator has excellent low-frequency isolation performance, and the isolation frequency band will decrease about 20 Hz when the isolated mass is fixed at 1.535 kg, compared with a similar circular linear isolator. These static and dynamic properties are well verified through experiments. Our work provides an innovative approach for the low-frequency vibration isolation and has wide potential applications in aeronautics.

Origami-inspire quasi-zero stiffness structure for flexible low-frequency vibration isolation

As an emerging technology, origami exhibits rich nonlinear static and dynamic properties. However, simulating creases remains a key challenge hindering practice application, especially for volumetric (deformable) origami. Inspired by the bistable behavior and axial-rotational coupling mechanism of triangulated cylindrical origami (TCO), this paper proposes a novel combined truss-spring structure with additional inertial mechanism (TCTS-RIM) for low-frequency vibration isolation. Unlike pure TCO, the TCTS-RIM uses elastic linkages to simulate all creases and modifies crease positions, enhancing physical realization in engineering applications and offering tunable stiffness and inertia on demand. Static analysis shows the modified truss-spring structure in TCTS-RIM has superior quasi-linear negative stiffness compared to pure TCO, which enables a very wide quasi-zero stiffness (QZS) range via linear spring compensation. The wide QZS range for different loads can be realized by setting appropriate structural parameters. From system dynamic equations, nonlinear inertia, nonlinear quadratic force, and nonlinear damping due to RIM are identified and discussed. The Alternating frequency–time harmonic balance method is used to obtain the displacement transmissibility, and its parametric influencing investigations verify that the proposed TCTS-RIM has excellent low-frequency vibration isolation performance and rich tunability. Comparative discussions show the wide QZS range significantly reduces the resonance frequency, broadens the isolation frequency band, and yields superior dynamic performance versus pure TCO isolators. Moreover, equivalent mass, anti-resonance and softening behavior induced by the rotational inertia mechanism further enhance low-frequency vibration isolation performance. An experimental prototype is built, and experimental results validate the correctness of the theoretical analyses. This work presents a simple mechanical implementation of volumetric origami, which may progress the engineering applications of origami and provide a viable approach to low-frequency vibration control.

Gas-Spring Quasi-Zero Stiffness Air Damping Isolator for Vertical Vibration Control of Indoor Substation Excited by Metro Loads

To mitigate the metro-induced vertical vibration of the indoor substation structure, this study proposes a gas-spring quasi-zero stiffness air damping isolator (AD-QZSI) with excellent low dynamic stiffness and high-static stiffness characteristics. The working principle and mechanical properties of the AD-QZSI are introduced and studied through theoretical and numerical methods. A model for substation considering soil–structure–equipment interaction is established using the software ABAQUS, its accuracy is validated based on a series of measured data from actual projects, and the AD-QZSI’s simulation method and parameter design method are described in detail. The air damper’s stiffness [Formula: see text] is integrated into the isolator’s mechanical model, theoretically and numerically achieving an accurate simulation of AD-QZSI’s nonlinear mechanical properties. The numerical results have an error of less than 5% with the measured data, indicating that the model is able to better capture the actual structure’s dynamic characteristics and is reasonable to be employed for subsequent analysis. Numerical results show that AD-QZSI can significantly reduce the structural vertical vibration, and its control effect is better in the whole frequency band, in particular, the effect is also visible in the low-frequency band, indicating that its vibration isolation frequency band is wider than that of traditional QZS isolator. With the vibration source distance increasing, the control effect of AD-QZSI presents a tendency to decrease and then level off, and its vibration isolation gain is weakened by the continuous increase of the damping ratio greater than 0.01. Moreover, the equipment’s dynamic amplification factor of the isolated structure decreases significantly. Finally, the proposed AD-QZSI can obtain ideal quasi-zero stiffness characteristics by adjusting the air pressure, and the adopted air damper belongs to the green low-carbon components, featuring great practical value and application prospects.

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.

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.

Elastic wave manipulation via functional incorporation of air-solid phases in hybrid TPMS

The TPMS metamaterial show extraordinary potential in shock absorption and noise reduction duo to the intricate porous configurations. In this study, a smooth-transition hybrid TPMS with multi-functional characteristics is designed to improve the performance of conventional hybrid materials, where multiple materials are stacked simply. The smooth hybrid intervals of proposed hybrid TPMS provide desirable transmission and reflection of stress wave conforming to the impedance characteristics of each component. Furthermore, the air domains in TPMS structure expand the high-frequency acoustic isolation properties. The broadening and customizing of isolation frequency band can be realized in the hybridizations. The mechanics-acoustics coupling property of proposed hybrid TPMS may have significant implications for the development of novel shock absorption and noise reduction materials.

Application of periodic structural wave impeding block for vibration isolation in foundation

The wave impeding board (WIB) is frequently integrated beneath dynamic machinery, tracks, and subgrades to counteract vibrations emanating from artificial sources. However, conventional WIBs have exhibited a limited isolation frequency band due to their dependence on the soil cut-off frequency of soil. Furthermore, the vibration sources typically encompass intricate frequency components spanning low, medium, and high frequencies. To overcome the technical limitations of WIBs relying on the cut-off frequency of soil, a new periodic structural wave impeding board (PSWIB) is proposed based on the principles of phononic crystals. Theoretical and numerical analyses demonstrate that PSWIB exhibits bandgap characteristics, with the attenuation range achieved by finite periodic structures aligning with the bandgap of an infinite PSWIB. Maximum amplitude reductions of 47 dB and 65 dB are achieved within the vibration attenuation range. Compared to traditional WIB, PSWIB surpasses the constraints imposed by the cut-off frequency of soil and allow for the design of constituent parameters based on the characteristics of the vibration source, enabling effective isolation of the target frequency vibrations.

Shock Isolation of an Orthogonal Six-DOFs Platform With High-Static-Low-Dynamic Stiffness

Abstract A novel approach to enhance the shock vibration environment of multi-directions using a high-static-low-dynamic stiffness supported orthogonal six-degrees-of-freedom (DOFs) nonlinear vibration isolation (OSNVI) system is presented in this paper. By combining spring positive stiffness and magnetic negative stiffness, the proposed system achieves high-static-low-dynamic stiffness. Under the multi-directions half-sine vibration, the dynamic equation of the OSNVI is obtained. Both dynamic and static analysis methods are utilized to explore the effect of various parameters on the shock isolation performance of the OSNVI from both the time and frequency domains. The results indicate that the proposed OSNVI can efficiently suppress multi-direction shocks at the cost of only one second. Although a nonlinear jump is usually not expected, the nonlinear jump of the OSNVI could improve the load capacity by increasing the spring stiffness without changing the shock isolation frequency band. Finally, a shock experiment is employed through a three-axis shaker platform to validate the shock isolation performance of the orthogonal six-DOF nonlinear vibration isolator. The proposed OSNVI provides a promising approach to suppress the multi-directional shock vibrations.

A combined vibration isolation system with quasi-zero stiffness and dynamic vibration absorber

The vibration control performance of a combined vibration isolation (CVI) system consists of a quasi-zero stiffness (QZS) system and a linear dynamic vibration absorber (DVA) is investigated. Firstly, the dynamic equation is established and the amplitude-frequency response of the CVI system is deduced by the harmonic balance method, and the analytical result is verified by numerical simulation. Secondly, the mechanism of CVI system is revealed from the perspectives of vibration amplitude, energy, and force transmission: The vibration isolation performance of the QZS system can be improved by reducing the vibration amplitude. Thirdly, the control performance of the CVI system is analyzed in terms of the effects of the stiffness, damping, mass ratio of DVA, and the damping of the primary system, as well as the robustness of the system. The findings lead to the development of an explicit tuning rule for the DVA attached to the QZS system. Lastly, a comparison of control performance with other three models is conducted. The results demonstrate that the CVI system can effectively suppress the vibration amplitude and broaden the isolation frequency band. The mechanism and tuning rule for the CVI system presented in this paper provides a useful reference for improving the control performance of the QZS system.

Dynamics and isolation performance of a vibration isolator with a yoke-type nonlinear inerter

Previous studies have shown that nonlinear inerters can achieve superior vibration suppression compared to linear inerters, such as broadening the effective frequency band of the vibration isolator. However, nonlinear inerters are typically implemented by incorporating linear inerters into nonlinear configurations, resulting in indirect configurations and extra connections. This study introduces a direct and simple way to realize a yoke-type nonlinear inerter by employing the Scotch yoke mechanism, which is named the Scotch yoke inerter (SYI). The primary contributions of this paper are introducing a concept about the physical realization of a nonlinear inerter capable of providing both apparent mass and nonlinear inertial effects and investigating the dynamic responses and isolation performances of a vibration isolator enhanced by the proposed nonlinear inerter. The working mechanism for how the proposed SYI generates the nonlinear inertia is introduced and a simple configuration that facilities the application of this nonlinear inerter is proposed. The mechanical model of the SYI is built to describe its inertial behavior using the Euler-Lagrange method. Then, the SYI is incorporated into a vibration isolator to improve its performances. The averaging method is adopted to obtain the analytical responses and dynamic characteristics of the isolator with SYI subjected to force excitation. The stability of this nonlinear isolator is analyzed, and numerical integration using the fourth-order Runge-Kutta method is employed to verify the analytical results. The isolation performance evaluation of the isolator with SYI is conducted through three indices including the peak dynamic displacement, peak force transmissibility and effective isolation frequency band. The mechanical behavior indicates that the SYI can successfully generate the apparent mass effect of an inerter and nonlinear inertial behavior. The analytical responses agree well with the numerical results for different parameters of the isolator with SYI, which verifies the analytical solutions. The use of SYI in the vibration isolator can bend the backbone curve to the low frequencies, which indicates the softening characteristic of the frequency response. The isolator with SYI demonstrates beneficial performances in terms of force transmissibility and effective isolation frequency band. It is concluded that the proposed SYI can be seen as an alternative nonlinear inerter and is beneficial for improving the performance of the vibration isolator.

Modeling and characteristics study of double-diamond bionic vibration isolation system with inerter

An integrated and bionic passive vibration isolation system is proposed based on the double-diamond bionic structure and inerter to solve the problems of poor low-frequency vibration isolation performance, narrow vibration isolation frequency band, and big additional mass of current passive vibration isolation system. To analyze the low-frequency vibration isolation performance and the valuable frequency band, the nonlinear dynamic model of the system is established, then the system transmission characteristics and stability are studied. It is found that the system can reduce the amplitudes of resonant peaks, broaden the valuable frequency band, and the system stability is excellent. Seen from the performance analysis, the introduction of the inerter with smaller additional mass makes the system have better vibration isolation performance and wider effective vibration isolation frequency band. The proposed system provides a new solution for vibration control in practical engineering.

Transverse vibration of axially loaded beam with parallel-coupled nonlinear isolators

To improve low-frequency vibration isolation when the excitation source and the isolation object are not co-located, transverse vibration of axially loaded beam with parallel-coupled nonlinear isolators is explored both experimentally and analytically. The nonlinear isolators use double annular magnets and spiral springs aligned on the same axis to achieve high static and low dynamic stiffness, which is suitable for low-frequency vibration isolation. Using the Galerkin truncation, harmonic balance analysis, and arc-length continuation, an approach is developed to analyze the frequency response functions of power flow for the strongly nonlinear discrete and continuum coupled systems. Both analytical and numerical results demonstrate that frequency response function of power flow can be used to deal with transverse vibration which excitation source and isolation object are not co-located. Parallel-coupled nonlinear vibration isolator can decrease the energy transmission of high order modal vibration of continuum, compared with the discrete isolation system. The axially loaded beam with parallel-coupled nonlinear isolators achieves significant vibration suppression at low frequency. Parametric studies of strongly nonlinear discrete and continuum coupled systems demonstrate that increasing the length of the beam and increasing the initial axial force can reduce the resonant frequency, which broadens the vibration isolation frequency band. An experiment is implemented to verify the accuracy of the theoretical model.

Design of micro-vibration suppression platform based on piezo-stack array intelligent structure

Micro-vibration seriously affects the precision and stability of precision mechanical systems. Aiming at the micro-vibration existing in the semiconductor package positioning system, this paper first designed an active-passive integrated actuator (APIA) based on piezo-stack array, which compensated the mechanical error through the piezo-stack array to improve its positioning accuracy. Based on the APIA, a 6-PUU parallel micro-vibration suppression platform (MVSP) was designed, in which the two APIAs were combined into one and installed on the lower platform along the tangential distribution of the circle, and then the kinematic model of the platform was established. Finally, the PID control algorithm was used to conduct vibration isolation experiments on the MVSP. The experimental results showed that the MVSP had good vibration isolation performance for micro-vibration, the vibration isolation frequency band was above 5 Hz, and the attenuation of micro-vibration signals was between 18% and 64%.

Sliding-boundary-constrained cantilever structure for vibration isolation via nonlinear stiffness modulation

In this paper, a novel sliding-boundary-constrained cantilever structure with nonlinear stiffness modulation (SCS-NSM) is proposed and systematically investigated for vibration isolation. The SCS-NSM is composed of a hemisphere-constrained cantilever structure (HCCS) and a pair of repulsive magnets. The nonlinear stiffness modulation mechanism for achieving quasi-zero stiffness (QZS), that is, using the hardening stiffness of the magnets to modulate the negative stiffness of HCCS, is fully revealed by static analysis. Furthermore, the QZS is adjustable to respond to different loads, and the modulation principle is clarified. Compared with conventional QZS isolators (paralleling negative and linear stiffness), the proposed SCS-NSM shows the advantages of wide load range and small static deflection. Static tests are performed to verify the effectiveness of the nonlinear stiffness modulation mechanism. Dynamic analysis shows that the SCS-NSM has a low resonant frequency and a wide vibration isolation frequency band due to its low stiffness. Periodic, sweep and random excitation tests are implemented to evaluate the vibration isolation performance of SCS-NSM. Experimental results validate the dynamic model and demonstrate that the vibration with a frequency higher than 4.6 Hz can be effectively attenuated. The proposed SCS-NSM provides a new perspective on low-frequency vibration isolation, and the nonlinear stiffness modulation mechanism has reference significance for designing QZS isolators with wide-bearing capacity and high compactness.

Performance of Downlink and Uplink Integrated Sensing and Communications (ISAC) Systems

This letter analyzes the fundamental performance of integrated sensing and communications (ISAC) systems. For downlink and uplink ISAC, the diversity orders are analyzed to evaluate the communication rate (CR) and the high signal-to-noise ratio (SNR) slopes are unveiled for the CR as well as the sensing rate (SR). Furthermore, the achievable downlink and uplink CR-SR regions are characterized. It is shown that ISAC can provide more degrees of freedom for both the CR and the SR than conventional frequency-division sensing and communications systems where isolated frequency bands are used for sensing and communications, respectively.

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

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

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

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

Stable decoding of working memory load through frequency bands

ABSTRACT Numerous studies have shown that working memory modulates every frequency band’s power in the human brain. Yet, the question of how the highly distributed working memory adapts to external demands remains unresolved. Here, we explored frequency band modulations underlying working memory load, taking executive control under account. We hypothesized that synchronizations underlying various cognitive functions may be sequenced in time to avoid interference and that transient modulation of decoding accuracy of task difficulty would vary with increasing difficulty. We recorded whole scalp EEG data from 12 healthy participants, while they performed a visuo-spatial n-back task with three conditions of increasing difficulty, after an initial learning phase. We analyzed evoked spectral perturbations and time-resolved decoding of individual synchronization. Surprisingly, our results provide evidence for persistent decoding above the level-of-chance (83.17% AUC) for combined frequency bands. In fact, the decoding accuracy was higher for the combined than for isolated frequency bands (AUC from 65.93% to 74.30%). However, in line with our hypothesis, frequency band clusters transiently emerged in parieto-occipital regions within two separate time windows for alpha-/beta-band (relative synchronization from approximately 200 to 600 ms) and for the delta-/theta-band (relative desynchronization from approximately 600 to 1000 ms). Overall, these findings highlight concurrent sustained and transient measurable features of working memory load. This could reflect the emergence of stability within and between functional networks of the complex working memory system. In turn, this process allows energy savings to cope with external demands.