Ultra-low Frequency Vibration Research Articles

An innovative design of parabolic cam-roller quasi-zero-stiffness isolators for ultralow frequency vibration isolation

An innovative design of parabolic cam-roller quasi-zero-stiffness isolators for ultralow frequency vibration isolation

Ultralow-Frequency Tip-Enhanced Raman Scattering Discovers Nanoscale Radial Breathing Mode on Strained 2D Semiconductors.

Collective excitations including plasmons, magnons, and layer-breathing vibration modes emerge at an ultralow frequency (<1 THz) and are crucial for understanding van der Waals materials. Strain at the nanoscale can drastically change the property of van der Waals materials and create localized states like quantum emitters. However, it remains unclear how nanoscale strain changes collective excitations. Herein, ultralow-frequency tip-enhanced Raman spectroscopy (TERS) with sub-10nm resolution under ambient conditions is developed to explore the localized collective excitation on monolayer semiconductors with nanoscale strains. A new vibrational mode is discovered at around 12 cm-1 (0.36 THz) on monolayer MoSe2 nanobubbles and it is identified as the radial breathing mode (RBM) of the curved monolayer. The correlation is determined between the RBM frequency and the strain by simultaneously performing deterministic nanoindentation and TERS measurement on monolayer MoSe2. The generality of the RBM in nanoscale curved monolayer WSe2 and bilayer MoSe2 is demonstrated. Using the RBM frequency, the strain of the monolayer MoSe2 on the nanoscale can be mapped. Such an ultralow-frequency vibration from curved van der Waals materials provides a new approach to study nanoscale strains and points to more localized collective excitations to be discovered at the nanoscale.

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.

Ultra-low frequency vibration energy harvesting of piezoelectric vibration systems with an adjustable device

Energy harvesting from external Ultra-low frequency vibrations is currently attracting a lot of attention. However, for the same system, it is difficult to satisfy the need for more efficient energy harvesting in a variety of external environments. Accordingly, an adjustable gearing device connected to the energy harvesting system is used herein for adapting energy harvesting to a wide range of external environments. The device uses four symmetrical inclined springs. One end of the springs is connected to a gear and the other end to a mass element. The geometrical parameters of the system can be varied by rotating the gears, thus varying the dynamic stiffness of the system. The kinetic equations of the system are derived and their nonlinear terms are Taylor-expanded. The amplitude-frequency response curve of the system is obtained by solving using the harmonic balance method. Multi-color plots of RMS values of induced voltage and electric power are obtained using the fourth-order Runge-Kutta method. The results show that the device has excellent adjustable performance. Adjusting the rotation angle of the gears can change the soft and hard characteristics of the system's dynamic stiffness and the intrinsic frequency, thus improving the system's energy harvesting performance in different environments.

Resonant-pillar-type acoustic black hole for ultralow-frequency vibration reduction

Abstract This paper proposes a resonant-type acoustic black hole (ABH). The ABH is achieved with gradient refractive index varies from the center of the lens to its outer surface. The performance of wave focusing and vibration reduction via the ABH is explored theoretically and numerically. Results show that the designed ABH can achieve wave focusing inside the lens and provide good vibration reduction at low frequency.

A high-performance electromagnetic energy harvester for scavenging ultra-low frequency vibration energy of human foot movement

A high-performance electromagnetic energy harvester for scavenging ultra-low frequency vibration energy of human foot movement

Limb-inspired quasi-zero stiffness structure for ultralow-frequency vibration attenuation

A bio-inspired limb-like vibration isolation structure is systematically studied by emulating the hexagonal skeletal configuration of animal legs under external loads and impact, which demonstrates a wide range of quasi-zero stiffness (QZS) characteristics. The dynamic model of the limb-like structure is established using Lagrange's equations to analyze the dynamical responses with QZS characteristics. The transmissibility of the system subject to periodic excitations is obtained by the Harmonic Balance Method and verified using the numerical integration method. In addition to the typical QZS, a unique configuration allows for a zero-stiffness feature throughout the entire stroke, enabling almost full-band frequency vibration isolation as the experimentally verified. Comparative analyses with a conventional QZS isolator prove the superior performance of the proposed structure, particularly in achieving full-band vibration isolation under zero-stiffness conditions. Furthermore, a novel QZS metamaterial, consisting of limb-like units, is modeled as a lumped-mass-spring chain. The linear and nonlinear analyses of the QZS metamaterial reveal that the QZS attribute lowers the cut-off frequency of the band structure. The diatomic QZS model generates a band gap in the ultralow frequency range attributed to the QZS and inertial amplification. Notably, this band gap can be tuned in real-time through pre-pressure adjustments, offering adaptability to variable engineering requirements.

Ultra-Low Frequency Vibration Isolation of Cockroach-Inspired Structures With Electromagnetic Shunt Damping Enhanced by Geometric Nonlinearity

Ultra-Low Frequency Vibration Isolation of Cockroach-Inspired Structures With Electromagnetic Shunt Damping Enhanced by Geometric Nonlinearity

Customized quasi-zero-stiffness metamaterials for ultra-low frequency broadband vibration isolation

Quasi-zero-stiffness (QZS) metamaterials play an important role in ultra-low frequency vibration mitigation. In this study, a customized QZS metamaterial is proposed to isolate ultra-low frequency broadband vibration and its isolation performance is verified. A representative unit cell (RUC) that satisfies both optimal QZS performance and minimum size is designed for the metamaterial and optimized by matching the parameters of positive stiffness heart-shaped beam with the properties of negative stiffness cosine beam. Then, a new composite structure with multiple RUCs is designed by matching the optimal mass block for each RUC to meet the vibration isolation requirements of ultra-low frequency and broadband. The transmissibility test is performed, and the isolator made of the metamaterial is then integrated into an underwater glider to test the vibration isolation performance. The results show that the proposed QZS metamaterial can isolate broadband vibrations of 3.2 to 60 Hz and the isolator can attenuate the vibration signals of gliders to the background noise in air and water. Therefore, the customized metamaterial can be used in the engineering case of ultra-low frequency broadband vibration isolation and the design method of the metamaterial can be used for reference by other equipment.

Ultralow-Frequency Vibration Sensing in Phase-Sensitive OTDR Using Multiscale VMD

Ultralow-Frequency Vibration Sensing in Phase-Sensitive OTDR Using Multiscale VMD

Archery-inspired catapult mechanism with controllable energy release for efficient ultralow-frequency energy harvesting

Ultralow-frequency (< 5 Hz) vibration energy is abundant in the environment, but its efficient utilization is still highly difficult due to the frequency-mismatch problem encountered by the vibratory energy harvesters and the slow rotation of rotary energy harvesters (REHs). To solve this issue, we developed herein a high-performance REH (named AI-REH) based on the archery-inspired catapult mechanism, which breaks through the limitation of the slow vibration source to the REH rotation speed through an innovative magnetic coupling strategy between the vibration source and the AI-REH. By employing an accumulator spring as the energy reservoir, the AI-REH also realizes the accumulation and controllable release of ultralow-frequency vibration energy via the interaction between the magnetic coupling and the elastic force. High-speed kinetic energy can thus be acquired for efficiently powering the rotor, contributing to significantly accelerated rotor speeds and enhanced electric outputs. Compared with the traditional counterpart, the AI-REH achieves 3.6-fold increase in rotor speed, 3.5-fold increase in output voltage and 3.0-fold increase in output power under an ultralow-frequency vibration of 4 Hz. A power backpack was also constructed and tested, which demonstrates the superior capability of the AI-REH in harnessing real ultralow-frequency amplitude-varying vibration energy. The AI-REH proposed in this study provides a new pathway for efficiently exploiting environmental ultralow-frequency vibration energy toward self-sufficient systems with various purposes.

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.

The X-shaped structure with nonlinear positive stiffness compensation for low-frequency vibration isolation

X-shaped structure with quasi-zero stiffness (QZS) properties are suitable for low-frequency vibration isolation because of its simple structure. The effective working range of classic X-shaped structure (CXS) is narrow for the existence of negative stiffness region, and using positive stiffness compensation to overcome this deficiency is a common way. This paper proposes a novel nonlinear positive stiffness compensation method (NPSC) to improve the load capacity and QZS range of CXS. Different from the previous studies that utilize linear or hardening stiffness compensation, the NPSC exhibits the characteristics of softening stiffness first and then hardening stiffness and is provided by torsion springs simply. The static properties of X-shaped structure with NPSC are investigated. The result indicates the NPSC possesses dual significant advantages. Firstly, the X-shaped structure with NPSC can achieve larger load capacity and wider QZS range than that with linear or hardening stiffness compensation in optimal parameter region. Secondly, the X-shaped structure with NPSC can conveniently overlap the equilibrium position with QZS point to obtain ultra-low frequency vibration isolation effect compared to that with linear stiffness compensation. The motion equation of the proposed system is derived, and the dynamic response is solved through harmonic balance method (HBM). The influence of different parameters on displacement transmissibility is investigated and the result is verified by numerical simulation. The transmissibility comparison between the proposed model and the CXS with linear compensation shows that the proposed model possesses better vibration isolation performance. Besides, the static compression test and dynamic sweep frequency experiment are implemented, and the experiment results verify the validity of proposed model. The proposed NPSC is an important inspiration for the stiffness compensation research of X-shaped structures.

An asymmetric bistable vibro-impact DEG for enhanced ultra-low-frequency vibration energy harvesting

In order to enhance the performance of bistable energy harvesters with dielectric elastomers (DEs) under ultra-low frequency vibrations, this paper proposes an asymmetric bistable vibro-impact dielectric elastomer generator (ABVI DEG), which mainly consists of a vibro-impact (VI) DEG, two identical pre-compressed springs, two pairs of undeformed springs, and a base. Two kinds of dynamics models of the proposed energy harvester under ultra-low frequency harmonic excitations are developed, and the instantaneous impact model is selected due to its computational efficiency and accuracy. The instantaneous impact model is extended by a series of impact experiments and validated by comparing the dynamical responses of the proposed energy harvester obtained from the two kinds of dynamics models. On this basis, the dynamical behavior and the energy harvesting (EH) performance of the proposed energy harvester under ultra-low frequency harmonic excitations are studied for the initial conditions of the system, different bistable potential wells, and various parameters, which include the pre-stretched ratio of the membranes and the distance between the two membranes. A further comparative study demonstrates the superiority of the proposed energy harvester under the ultra-low frequency harmonic excitation. This work not only provides an insight into dynamical behavior of the proposed ABVI DEG, but helps guide the design and optimization of the proposed EH system in the ultra-low frequency vibration environment.

Ultra-low frequency vibration isolation of a novel click-beetle-inspired structure with large quasi-zero stiffness region

Inspired by the three postures of a click beetle, a novel passive click-beetle-inspired structure (CBIS) with variable asymmetric stiffness characteristics is proposed and systematically investigated for stiffness tunning and low-frequency vibration isolation. The main structure of CBIS is consisted of three rods and two springs but the geometrical nonlinearity and stiffness properties are abundant. Based on the Lagrange principle, the stiffness properties of CBIS is analyzed comprehensively for the unbending posture, down-bending posture and up-bending posture, respectively. The corresponding displacement transmissibility derived with the harmonic balance method. The hardening and softening stiffness phenomenon may occur by tuning geometric parameters. The stiffness can be tuned easily among negative, quasi-zero, zero, small positive by the initial assembly angle, length ratio and linear stiffness ratio. The zero stiffness (ZS) or quasi-zero stiffness (QZS) region can be extremely huge under some special parameters, which can broaden the working range of CBIS and benefit to large-deflection vibration isolation. The peak transmissibility can be reduced to 7 dB or even 0 dB and the resonant frequency can be smaller than 2 Hz, which is conductive to ultra-low frequency vibration isolation. The proposed CBIS opens a new route towards tunning asymmetric stiffness for low frequency vibration isolation.

A semi-active electromagnetic quasi-zero-stiffness vibration isolator

A semi-active electromagnetic quasi-zero-stiffness (QZS) vibration isolator (VI) (SEQZS VI) is proposed to broaden the frequency bandwidth for low or ultra-low frequency vibration isolation. The electromagnetic negative stiffness mechanism (NSM) applies a newly designed "8"-shaped electromagnetic equivalent magnetic circuit and has a more extensive tunable range of negative stiffness (NS) than previous studies. Moreover, theoretical formulations for the SEQZS VI in static and dynamic analyses under harmonic excitations were derived in detail and the parameter analysis is carried out to provide a reference for the design. Furthermore, a prototype is fabricated and tested to validate the design concept of SEQZS VI. The experimental results validate the present formulation and show that the vibration isolation performance of the proposed SEQZS VI is much better than that of the corresponding linear isolator. Moreover, the present SEQZS VI can have lower stiffness in a wider region and lower transmissibility at the resonance frequency.

Enhancing the Bandwidth and Energy Production of Piezoelectric Energy Harvester Using Novel Multimode Bent Branched Beam Design for Human Motion Application.

In recent years, harvesting energy from ubiquitous ultralow-frequency vibration sources, such as biomechanical motions using piezoelectric materials to power wearable devices and wireless sensors (e.g., personalized assistive tools for monitoring human locomotion and physiological signals), has drawn considerable interest from the renewable energy research community. Conventional linear piezoelectric energy harvesters (PEHs) generally consist of a cantilever beam with a piezoelectric patch and a proof mass, and they are often inefficient in such practical applications due to their narrow operating bandwidth and low voltage generation. Multimodal harvesters with multiple resonances appear to be a viable solution, but most of the previously proposed designs are unsuitable for ultralow-frequency vibration. This study investigated a novel multimode design, which included a bent branched beam harvester (BBBH) to enhance PEHs' bandwidth output voltage and output power for ultralow-frequency applications. The study was conducted using finite element method (FEM) analysis to optimize the geometrical design of the BBBH on the basis of the targeted frequency spectrum of human motion. The selected design was then experimentally studied using a mechanical shaker and human motion as excitation sources. The performance was also compared to the previously proposed V-shaped bent beam harvester (VBH) and conventional cantilever beam harvester (CBH) designs. The results prove that the proposed BBBH could harness considerably higher output voltages and power with lower idle time. Its operating bandwidth was also remarkably widened as it achieved three close resonances in the ultralow-frequency range. It was concluded that the proposed BBBH outperformed the conventional counterparts when used to harvest energy from ultralow-frequency sources, such as human motion.

Low and ultra-wide frequency wave attenuation performance and tunability of a new cruciate ligament structure

This paper presents two novel cruciate ligament structures with outstanding contributions in lightweight design of metamaterials, band gap tuning, and ultra-wide and ultra-low frequency vibration and noise reduction, as well as providing a new design idea. The novelty of this paper is manifested in various aspects, combining Bloch's theorem and finite element method to calculate the band gap, and using the transfer function to verify the evaluation; using structural optimization and applying active strain to test the structural tunability; and illustrating the wave propagation and band gap opening mechanism from the vibration mode and energy perspectives. The results show that the widest band gap can reach 5061.9 Hz after structural optimization and tuning, while the lowest can be reduced to 274.3–285.6 Hz, and the vibration attenuation peak is around −620, so the structure has excellent vibration and sound insulation effect, while the band gap can be widened and reduced under active strain. The opening of the band gap is closely related to the directionality and regionality of wave propagation, and the comprehensive analysis method of wave propagation provides innovative research ideas for wave propagation, and also provides theoretical and technical support for structure and band gap optimization.

A tunable multi-arm electromagnetic pendulum for ultra-low frequency vibration energy harvesting

Autonomous electronic devices and sensors are essential to reduce expensive maintenance, increasing job security and reliability, avoiding battery replacements and wired systems. Industrial systems and civil structures vibrate dissipating an important amount of energy that can be harvested to power small devices. This work continues and extends a previous work from the authors (Castagnetti 2019 Meccanica 54 749–60). Here we improved that initial configuration by proposing a tunable multi-arm electromagnetic pendulum for ultra-low frequency vibrations energy harvesting. This configuration features five electromagnetic converters and a magnetic spring, each supported by a pendulum arm with different length: when excited by external vibrations, this six arms frame is free to oscillate around a central pivot. The paper starts from conceptual design, includes a detailed multiphysics dynamic simulation implemented with Matlab Simscape software, presents the prototype development through three-dimensional printing and experimental validation. Systematic experimental tests investigated different pendulum configurations for three stiffness levels of the magnetic spring and confirmed both the ultra-low frequency response (from 2 to 10 Hz), as predicted by the dynamic simulation, and the good voltage and power outputs. Specifically, for the higher stiffness of the magnetic spring, corresponding to an oscillation frequency of about 9.5 Hz, the power output was up to 8.4 mW and the output voltage of about 2 Volt.

Metamaterial beams with graded two-stage inertial amplification and elastic foundation

In this study, a novel local resonant metamaterial (LRM) beam with elastic foundation is proposed by introducing grounded local resonators based on the two-stage inertial amplification structure with adjustable large inertia. The complex band structure is calculated by using the extended plane wave expansion method, and it is found that bandgaps of the novel LRM beam are lower and wider than that of the existing inertant LRM beam. The formation mechanisms of such bandgaps are revealed, and the effects of structural parameters on bandgap characteristics are discussed. Numerical analysis and experimental measurement of vibration transmission characteristics of finite beam structure verify the accuracy of the theoretical results. Furthermore, three kinds of bandgap widening methods based on the structure tunability of local resonator are proposed by setting graded structural parameters. The regularities of bandgap variation with different parameter spacings are given, and the effectiveness of the method is verified by numerical analysis of the finite graded LRM beam under different boundary conditions. These results are expected to provide certain guidance for low and ultra-low frequency broadband flexural waves and vibration control.