Vibration Attenuation Research Articles

Numerical analysis of energy dissipation due to eddy currents in a vibrating beam

Vibration attenuation is a key aspect of mechanical engineering. One method to achieve this is through eddy currents, which can be generated in a vibrating system when a magnetic field is present, creating forces that oppose motion. This study examines a mechanical system consisting of a thin cantilever beam vibrating in a uniform and time-invariant magnetic field under steady-state conditions to understand the nature of energy dissipation and the relationship between motion, eddy currents, and damping forces. The calculation of eddy currents generally requires the use of complex numerical procedures. However, for systems with simple geometry, such as a cantilever beam, a recent numerical procedure based on the finite difference method, known for its simplicity in implementation, has been adapted and expanded to determine eddy currents under motional induction. A numerical application has been developed in which the vibration of a specific beam is characterised by its bending or torsional mode shapes, and the nature of the corresponding dissipative forces is analysed. Results indicate that the eddy currents are an effective means of dissipating energy at lower-order modes. Additionally, the direction of the applied magnetic field can induce coupling between bending and torsional vibrations.

Realization of topological Bragg and locally resonant interface states in one-dimensional metamaterial beam-resonator-foundation system

Abstract In this study, the one-dimensional (1D) metamaterial beam-foundation system is innovatively improved into a metamaterial beam-resonator-foundation system by inserting resonators into the elastic foundation for ultra-low frequency vibration attenuation and enhanced topological energy trapping. Abundant band gap characteristics are obtained including quasi-static band gap starting from 0 Hz, Bragg scattering band gaps (BSBGs), and local resonance band gaps (LRBGs). Five band folding points are obtained through the band folding mechanism which can be opened by tuning inner and outer resonance parameters. However, only three band folding induced band gaps support mode inversion and Zak phase transition, including one BSBG and two LRBGs. The topological inversion in LRBGs is rarely reported in the 1D mechanical system, which can induce topological locally resonant interface states. The underlying physical mechanism of the topological phase transition in LRBG is revealed, which results from the topological inversion band gap transition from an initial BSBG to a LRBG with resonance parameters changes. Different from conventional 1D topological metamaterials that merely utilize local resonance to lower the band frequency and achieve subwavelength topological states in BSBGs, the topological interface states in LRBGs can localize wave energy to fewer unit cells near the interface, exhibiting enhanced energy localization capacity. The topologically protected interface states are validated with defective cases, demonstrating the potential of topological metamaterials for robust energy harvesting. This study provides new insights into the topological theory of 1D mechanical systems and contributes to the development and implementation of multi-functional devices integrating vibration attenuation and energy trapping.

Topological modes, vibration attenuation, and energy harvesting in electromechanical metastructures

The dynamics of topological boundary modes in both periodic and quasi-periodic electromechanical metastructures is investigated, with a focus on their applications to energy harvesting and vibration reduction. The metastructure analyzed in this study is based on a shunted array of piezoelectric patches, with electrical parameters modulated according to the 1D Aubry–André–Harper model. As a result of this modulation, a fractal spectrum is generated near the central frequency of the resonators, a hallmark of nontrivial topology that enables the emergence of digitally controllable edge states and ensuing localization phenomena at subwavelength frequencies. In this framework, a detailed analysis of the metastructure spectral characteristics is conducted to investigate the influence of the modulation parameters on mode localization, both at the boundaries and within the interior of the beam. Such localization effects are then studied in relation to the energy harvesting, attenuation, and wave transport capabilities of the system. These functionalities point toward the realization of self-powered structures with low frequency and digitally controllable vibration attenuation capabilities, and are considered of significant technological interest in applications involving elastic waves and vibrations, where the ability to precisely control and harness these phenomena could lead to innovative solutions in energy-efficient and adaptive systems.

AI-driven optimization of dynamic vibration absorbers with hydraulic amplifier and mechanical inerter integration

Dynamic vibration absorbers (DVAs) have been widely employed in vibration suppression applications for decades. While DVAs offer an effective solution, they are limited by the need for a high mass ratio between the DVA and the primary system to achieve significant vibration attenuation. To overcome this, researchers have introduced lever mechanisms, allowing for enhanced vibration suppression without increasing the mass ratio. However, levers, commonly used as amplification mechanisms, suffer from high inertia and limited amplification, particularly in larger applications. Another limitation is when DVAs are employed for energy harvesting as a secondary objective, they exhibit high sensitivity to system parameter variations, requiring extensive optimization. Various optimization techniques have been applied to DVAs for multi-objective optimization, including fixed-point theory, which is complex and requires intensive mathematical derivation, and simple metaheuristic techniques such as genetic algorithms (GA). This study proposes four novel DVAs using a hydraulic amplifier (HA) to address the limitations of traditional lever mechanisms and a mechanical inerter to improve the vibration damping. Also, multi-objective optimization was performed using particle swarm optimization (PSO) which is considered innovative in this application and compared with commonly used genetic algorithms (GA). The governing equations were derived using Newton’s second law and solved numerically with the Runge-Kutta method. An AI-based approach was utilized for HA design. The results show that integrating HA and mechanical inerters significantly enhances vibration attenuation and broadens the frequency response. Additionally, the location of the mechanical inerter is critical in reducing vibration amplitude. Also, the multi-objective PSO outperforms GA in solution diversity and quality. The proposed integration of HA in DVAs offers potential applications across various engineering fields.

Analytical modeling of piezoelectric meta-beams with unidirectional circuit for broadband vibration attenuation

Broadband vibration attenuation is a challenging task in engineering since it is difficult to achieve low-frequency and broadband vibration control simultaneously. To solve this problem, this paper designs a piezoelectric meta-beam with unidirectional electric circuits, exhibiting promising broadband attenuation capabilities. An analytical model in a closed form for achieving the solution of unidirectional vibration transmission of the designed meta-beam is developed based on the state-space transfer function method. The method can analyze the forward and backward vibration transmission of the piezoelectric meta-beam in a unified manner, providing reliable dynamics solutions of the beam. The analytical results indicate that the meta-beam effectively reduces the unidirectional vibration across a broad low-frequency range, which is also verified by the solutions obtained from finite element analyses. The designed meta-beam and the proposed analytical method facilitate a comprehensive investigation into the distinctive unidirectional transmission behavior and superb broadband vibration attenuation performance.

Local resonance metamaterial-based integrated design for suppressing longitudinal and transverse waves in fluid-conveying pipes

To solve the problem of low broadband multi-directional vibration control of fluid-conveying pipes, a novel metamaterial periodic structure with multi-directional wide bandgaps is proposed. First, an integrated design method is proposed for the longitudinal and transverse wave control of fluid-conveying pipes, and a novel periodic structure unit model is constructed for vibration reduction. Based on the bandgap vibration reduction mechanism of the acoustic metamaterial periodic structure, the material parameters, structural parameters, and the arrangement interval of the periodic structure unit are optimized. The finite element method (FEM) is used to predict the vibration transmission characteristics of the fluid-conveying pipe installed with the vibration reduction periodic structure. Then, the wave/spectrum element method (WSEM) and experimental test are used to verify the calculated results above. Lastly, the vibration attenuation characteristics of the structure under different conditions, such as rubber material parameters, mass ring material, and fluid-structure coupling effect, are analyzed. The results show that the structure can produce a complete bandgap of 46 Hz–75 Hz in the low-frequency band below 100 Hz, which can effectively suppress the low broadband vibration of the fluid-conveying pipe. In addition, a high damping rubber material is used in the design of the periodic structure unit, which realizes the effective suppression of each formant peak of the pipe, and improves the vibration reduction effect of the fluid-conveying pipe. Meanwhile, the structure has the effect of suppressing both bending vibration and longitudinal vibration, and effectively inhibits the transmission of transverse waves and longitudinal waves in the pipe. The research results provide a reference for the application of acoustic metamaterials in the multi-directional vibration control of fluid-conveying pipes.

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.

Analysis of vibration signals near ground surface during blasting excavation of a tunnel in fractured rock

This study aims to analyze the vibration signals near the ground surface due to the underneath drilling and blasting activities in a fissured rock tunnel. Blasting induced vibration on the ground surface was continuously monitored in a fissured rock tunnel drilling and blasting excavation project in field. Wavelet packet analysis of the vibration signals using Matlab was carried out for signal denoising, differential blasting delay time interval identification, and three-way time-frequency energy analysis. The results show that within a 30 m range from the palm face, the dominant frequency bands of blasting-induced vibrations on the ground surface were concentrated in the range of 0–130 Hz. Two prominent peak frequency bands were identified at 31.25–39.063 Hz (low-frequency band) and 93.75–101.56 Hz (high-frequency band), accounting for 12% of the total energy. Among the three directions of ground surface vibrations, the energy decay was the most significant in the x-direction (tunnel excavation direction), which amounted to 54.29% of the overall energy decay with increasing distance. The energy decay within the 50–80 Hz range was the most pronounced (more than 90%), when the angle between the vibration propagation direction and the fissure or joint direction was 75°. The conclusions provide the insights in the attenuation of blast-induced vibrations in fissured rock and can potentially assist in the design of blasting vibration control.

Hygienic assessment of the protective properties of personal hand protection equipment during vibration testing

Introduction. In industrial environments, at the workplaces of hand tool operators, it is not always possible to completely eliminate increased levels of vibration exposure. The power and speed characteristics of modern hand-held machines are constantly increasing. The impact of local vibration on a person has a negative effect on his body. When working with hand tools, personal protective equipment is used. The purpose of personal hand protection against vibration is to reduce the vibration impact on a person. Materials and methods. Bench tests were carried out on hand protection products consisting of damping materials of various shapes and locations in the product. The vibration sensor was installed and fastened in places where the operator’s hands came into contact with vibration and on the forearm. The effectiveness of protection was determined by the difference in measurement levels. Results. During the tests, vibration levels were recorded on the handle of the vibration stand, the palmar surface, the fingers, and the operator’s forearm. In the low-frequency region of the spectrum, vibration attenuation is minimal, and as the frequency range increases, the attenuation increases. Across all areas of the spectrum, performance levels for mittens are higher than for gloves. In places where the fingers come into contact with vibration, the efficiency is less than when in contact with the hand, and in the low-frequency region of the spectrum a negative efficiency of up to 0.8 dB is noted. Vibration measurements on the operator’s forearm showed vibration levels in the forearm to be lower than in the hand. Limitations. The study was conducted over a period of one year, in laboratory conditions, and was limited to two thousand measurements. Conclusion. Hygienic assessment of the effectiveness of the protective properties of personal protective equipment for hands was carried out in accordance with developed laboratory test methods when installing and securing a vibration sensor on the handle, hand, and forearm of the operator. Determining the effectiveness of the entire product model should be considered when designing and manufacturing new hand protection against vibration.

Evaluation of the attenuation mechanism of the noise reduction performance of polyurethane porous elastic road surface

The polyurethane porous elastic road surface (PERS) demonstrates superior noise reduction performance, primarily due to its porous structure that facilitates effective sound absorption and its high elasticity that contributes to substantial vibration attenuation. However, it is susceptible to void clogging and long-term aging during service, leading to a gradual decline in noise reduction performance. To investigate the attenuation characteristics of noise reduction performance in PERS mixtures under void clogging and long-term aging conditions, this study investigated PERS mixtures subjected to various clogging cycles and aging times. Concurrently, the tire vertical drop test and standing wave tube absorption coefficient test were employed to analyze the variation rule in the noise sound pressure level (SPL) and sound absorption coefficient frequency curves under the above conditions. The results show that the noise reduction performance of the PERS mixture exhibits a variation rule of first decreasing and then increasing with the increase of the clogging cycles, and the required clogging amount to reach the void saturation state is 30–40 g. Compared to before clogging, the PERS mixture after clogging has an enhanced ability to absorb low-frequency noise and a weakened ability to absorb high-frequency noise; the sizes of the cloggings have a higher degree of attenuation in low-frequency sound absorption than in high-frequency. As long-term aging progresses, the noise reduction performance of the PERS mixture first increases and then decreases. Notably, long-term aging predominantly impacts the high-frequency noise reduction capabilities of the PERS mixture. The impact of void clogging on the noise reduction performance of PERS mixtures is found to be more pronounced than that of long-term aging.

Experimental study on the free and constrained vibration performance of composite wave springs

This article proposes a glass fiber reinforced plastic (GFRP) wave spring and conducts a study on its free and constrained vibration characteristics and compression performance. Initially, a stiffness prediction model for composite wave spring is established using laminated plate theory and Moore’s theorem. Additionally, the failure mode of the composite wave spring was predicted and experimentally confirmed using ABAQUS and the 3D-Hashin failure criterion. Finally, the vibration characteristics of composite wave spring and metal helical spring are investigated using the B&K testing system in both free and constrained states. The experimental stiffness and ultimate load of the composite wave spring are 20.67 N/mm and 1386.67 N. The composite wave spring exhibits good vibration reduction performance in both free and constrained states, with maximum vibration attenuation amplitudes of 122.71 and 144.93 dB. In comparison, the metal helical spring has maximum vibration attenuation amplitudes of 41.65 and 111.89 dB.

Easy to fabricate 3D metastructure for low-frequency vibration control

As a burgeoning category of elastic metamaterials, 3D metastructures have garnered significant research attention for manipulating low-frequency acoustic and elastic waves. Bandgap engineering allows for the control of these waves across a subwavelength ultrawide frequency range. However, the manufacturing of these 3D structures poses a challenge, necessitating additional support materials for 3D-printed components, creating difficulties in mass production. In this study, we propose a novel lightweight 3D metastructure design that is easy to fabricate and provides a low-frequency subwavelength bandgap. We replaced conventional struts supporting heavy mass inclusions in typical designs with modified arch beams. This structural modification enables the easy and self-supporting manufacturing of 3D metastructure unit cells without the need for extra support material. Utilizing magnets and steel masses with bolts as hard inclusions, the magnet facilitates the quick assembly of the 3D metastructure, potentially facilitating mass manufacturing in practical applications. The wave dispersion and bandgap properties of the metastructure are investigated numerically, and experimental vibration tests are performed on the 3D-printed and assembled parts. The experimental results and numerical findings demonstrate robust vibration attenuation at low frequencies by the proposed 3D metastructure. The suggested, easy-to-fabricate 3D-metastructure design holds potential applications in low-frequency elastic-wave manipulation, including noise and vibration control.

Fractal-fractional model for the receptor in a 3D printing system

A critical hurdle in three-dimensional printing is the low printing accuracy. In particular, the deformation of the printed object on the receptor makes accurate printing impossible due to insufficient solvent evaporation. We address this challenge by establishing a Murray-like receptor to control the morphology of the printed object, which can be used for accurate printing through efficient residual energy absorption and active vibration attenuation. A fractal oscillator is established and He’s frequency formulation is used to reveal the fractal response of the Murray-like receptor, and an experiment was carried out to show that the receptor system can keep the printed object in good shape without any deformation.

The coupled band gap of longitudinal wave in metamaterial-based double-rod containing resonators

This study investigates the coupled band gap and vibration propagation characteristics of elastic waves in a metamaterial elastic double-rod system with attached periodic resonators. We derive the band gap structure and vibration attenuation equations of double-rod structure using the spectral element method, Bloch’s theorem, and the transfer matrix method. The validity of the coupled band gap is confirmed through forced vibration response analysis. Furthermore, we examine the effects of various parameters on the double-rod system, revealing that coupled band gaps exist with the average vibration attenuation rates of −50.23 dB for rod one and −47.87 dB for rod two, respectively. Remarkably, by adjusting the double-rod parameters, both the band gap frequency range and vibration attenuation ability of the coupled band gap can be adjusted to meet specific engineering requirements in low-frequency regions. This research contributes to developing continuous mechanical structures featuring coupled band gaps.

Shaking table test of TLD/TLCD vibration control for offshore wind turbine support structure

In this research, a scale-model with a similarity-ratio of 1:15 is specifically designed for shaking table test based on a 6.45MW OWT (Offshore wind turbine). The scale-model is equipped with a TLD (Tuned liquid damper) at the top and a TLCD (Tuned liquid column damper) at 2/3 of its height. Various external excitations with distinct spectral characteristics are applied to analyze the vibration characteristics of the OWT and the damping performance of the TLD/TLCD. The results indicate that the dynamic characteristics satisfy the similarity-ratio between the prototype-model and scale-model. The acceleration response of the OWT is significantly influenced by the external excitation spectrum, whereas the displacement response is primarily governed by the model 1st-order natural-frequency. With the mass eccentricity applied at the tower top and bidirectional excitation input, torsional deformation occurs in the tower, resulting in a ‘beat vibration’ phenomenon. Upon the incorporation of TLD/TLCD, the vibration response attenuation-ratio can reach up to 70 % under harmonic excitation, up to 25 % under seismic excitation and up to 50 % under equivalent base acceleration. After the implementation of vibration attenuation, there is a significant reduction in the time-domain response, and the rate of reduction is accelerated. In the frequency-domain response, the spectral peak at the natural-frequency disappears.

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.

Design and test of a contactless damper for HTS maglev systems via electromagnetic shunt dampers

High-temperature superconducting (HTS) maglev system is promising to become the future high-speed transport due to its numerous advantages. However, the low-damping dynamic characteristics of superconductors make the system vulnerable to external disturbances, which present a significant challenge to its implementation. To enhance the vibration attenuation effect of the HTS maglev system, a non-contact damper that employs electromagnetic shunt damping (EMSD) and negative resistance is incorporated into the HTS maglev system. This study elucidates the principles of EMSD and negative resistance, and establishes the governing equations to describe the behavior of the HTS maglev model equipped with EMSD. Subsequently, the EMSD coupling coefficients are analysed via the finite element method (FEM) under varying conditions. Finally, a dedicated vibration test rig is designed and fabricated to validate the effectiveness of the proposed damper. The results demonstrate that the proposed damper, in combination with negative resistance, is capable of effectively suppressing vibration in HTS maglev systems. The maximum acceleration of the test model can be reduced by 86% compared with the original system without the damper. This work may provide valuable guidance for future practical implementations.

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.

Dynamic Characteristics of Pressure-Balanced Metal Bellows in Fluid–Structure Interaction

As a flexible component in high-pressure vessels and pipeline systems, bellows experience significant fluid–structure interaction effects under high-speed internal fluids and external vibrations. Nevertheless, their dynamic response mechanisms coupled with fluid–structure interaction mentioned below have not yet been clarified so far. In this work, a novel pressure-balanced metal bellow (PBMB) for low-stiffness and high-pressure resistance is firstly proposed. Several fluid–structure interaction models were considered to study the dynamic response characteristics of the PBMB. An experimental platform associated with fluid–structure interaction was established to validate the effectiveness of its vibration attenuation performance. The results indicate that the PBMB has an obvious vibration attenuation effect in the range of 5–90[Formula: see text]Hz, and super-harmonic and sub-harmonic resonance phenomena occur in the range of 90–200[Formula: see text]Hz. Under constant fluid conditions, fluid density, viscosity, flow velocity, and pressure are positively correlated with the response amplitude of the PBMB. The response of the PBMB oscillates at the fluid entry point due to both pulsating flow velocity and pulsating pressure. After several cycles, the response caused by pulsating flow velocity gradually decays and stabilizes. Thus, the impact of pulsating frequency on the stability of the response of bellows is insignificant during the initial cycles.

Topology optimization of adaptive sandwich plates with magnetorheological core layer for improved vibration attenuation.

In this study the optimum topology distribution of the magnetorheological elastomer (MRE) layer in an adaptive sandwich plate is investigated. The adaptive sandwich plate consists of an MR elastomer layer embedded between two thin elastic plates. A finite element model has been first formulated to derive the governing equations of motion. A design optimization methodology incorporating the developed finite element model has been subsequently developed to identify the optimum topology treatment of the MR layer to enhance the vibration control in wide-band frequency range. For this purpose, the dynamic compliance and density of each element are defined as the objective function and design variables in the optimization problem, respectively. The method of the solid isotropic material with penalization (SIMP), is extended for material properties interpolation leading to a new MRE-based penalization (MREP) model. Method of moving asymptotes (MMA) has been subsequently utilized to solve the optimization problem. The developed finite element model and design optimization method are first validated using benchmark problems. The proposed design optimization methodology is then effectively utilized to investigate the optimal topologies of the magnetorheological elastomer (MRE) core layer in MRE-based sandwich plates under various boundary and loading conditions. Results show the effectiveness of the proposed design optimization methodology for topology optimization of MRE-based sandwich panels to mitigate the vibration in wide range of frequencies.