Fig 4
Contexts in source publication
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... show the use of multi-frequency vibration absorbers to design broadband metamaterials, we consider the 3-DOF system shown in Fig. 4. The vibration absorber uses two lumped masses. The equations of motion are given ...
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... is well known that a dynamical system with low damping quickly responds to a transient excitation but slowly damps out the system 0 s vibration after the excitation stops. However, for the system shown in Fig. 4, a large c 2 can reduce the left and right peaks of jH 11 j in Fig. 6a, but it cannot reduce the middle peak and it increases the two lowest values of jH 11 j around ω 1 and ω 2 . Hence, a small value for c 2 is recommended. Moreover, to reduce the middle peak and to damp out the system 0 s vibration after the excitation stops, one can ...
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... isolators are different from vibration absorbers. For a vibration absorber, the loading point and the response point of main concern are on the same object (i.e., m 1 in Fig. 4). For a vibration isolator, the loading point and the response point of main concern are on different objects. A vibration isolator works by using the out-of-phase inertia force of the loaded object to reduce the load transferred to the response point, and it works best if the system 0 s damping is small and Ω 4 ffiffiffi 2 p ω (ω is ...
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... shown in Fig. 1, the goal is to design a metamaterial beam that can stop propagation of transverse elastic waves (mainly asymmetric Lamb waves) based on the use of the multi-frequency vibration absorber shown in Fig. 4. Because rotational vibration absorbers were shown to be inefficient [19], we consider only translational vibration absorbers in the free-body diagram of the unit cell model shown in Fig. 7a. The governing equation for a unit cell of an infinite metamaterial beam can be derived using the extended Hamilton principle R L 0 ðδT À δΠ þ δW ...
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Citations
... During the past few decades, acoustic metamaterials have attracted considerable attention and provided new ideas and solutions for the problems of science and engineering [1][2][3][4][5]. Acoustic metamaterials are artificial structures constructed by a periodic variation in the mechanical properties of materials [1]. ...
... The traditional locally resonant acoustic metamaterials mainly focus on the application of linear resonators to obtain low-frequency bandgaps [2,4]. However, the width of the band-gap is narrow and the attached mass of the vibration absorber are always heavy [29]. ...
This paper presents a metamaterial beam with the nonlinear magnetic mass-beam (NMMB) resonators to achieve certain tunable bandgaps. The metamaterial beam consists of the upper and lower faceplates and the periodically arranged NMMB resonators. The dispersion relation of the infinite-size beam is derived via the energy method. The governing equations of motion of the beam with finite length are obtained based on the Galerkin method. An experiment is designed and the revealed phenomena reach a good agreement with the theoretical analysis and numerical simulations. The results show that the tunable bandgaps are associated with the external excitation amplitude. As the amplitude of the excitation varies, the location and width of the bandgaps can be adjusted according to the frequency shift and multi-bandgap effects. Moreover, the influences of the thickness of the faceplates and the stiffness of cantilevers in the resonators on the bandgaps are shown.
... Concurrently, some researchers combine local resonators into honeycomb panels (Qi et al., 2019b), origami (Jiang et al., 2023a), metamaterial beams (Pai, 2010;Sun et al., 2010;Pai et al., 2014) to achieve accurate regulation of the target bandgap to improve the impact and vibration resistance of low frequency range (Jin et al., 2022). Li et al. (2023b) proposed an innovative special class of magnetorheological metamaterial to achieve a tunable band gap by using a new frequency feedback control law, which can make the active band gap intelligently track the external excitation frequency. ...
Local resonant metamaterials show significant promise in applications involving the attenuation of impact waves. This paper introduces a honeycomb metamaterial featuring a circular distribution of multiple mass-beam resonators designed to enhance impact mitigation by broadening low frequency bandgaps. The bandgaps of unit cells with different number of mass-beam resonators (MBR) are calculated. It is found that the unit cell with circularly distributed resonators (C-MBR) has strong low frequency local resonance in all directions, thus opening a complete wide bandgap in about 500-1200Hz. Then, a method of equivalent stiffness reduction related to the corresponding mode shapes is used to research the negative effective mass density characteristic, explaining the generation of the low frequency bandgaps. Subsequently, the impact protection capacity of local resonant metamaterial is compared with that of ordinary honeycomb metamaterial through experiment and simulation. Interestingly, the maximum acceleration values under the impact load of local resonant metamaterial are about 45% lower than that of honeycomb metamaterial, and the reaction force under the blast load is about 80% reduction. Besides, by analyzing the acceleration curve waveform and transmission spectrum, the local resonant metamaterial is found to exhibit continuous short period vibration, which blocks the wave in low frequency band. Finally, the energy dissipation performance of the local resonant metamaterial explains that it converts more impact energy into the kinetic energy of the core with resonators, thereby reducing the energy transferred to the bottom panel. These results underscore the potential application of the proposed metamaterial with multi-resonators in impact mitigation and energy dissipation.
... Due to excellent flexibility in design, numerous works have been carried out. Pai proposed a new metamaterial beam based on multi-frequency vibration absorbers for broadband vibration absorption [12]. Chen et al. [13] realized bandgap control in an active elastic metamaterial with negative capacitance piezoelectric shunting. ...
Metamaterials with high-static-low-dynamic stiffness (HSLDS) resonators possess the ability in low/ultra-low frequency flexural wave attenuation. However, the inherent geometrical nonlinearity of the HSLDS resonators was used to be neglected for simplicity, leading to severe restriction of its operating range. In this paper, the intrinsic geometric nonlinearity of the HSLDS resonator is considered to extend its applications. The nonlinear dynamic model of a metamaterial beam coupled with nonlinear HSLDS resonators is established based on the Galerkin method. An efficient frequency-domain analysis strategy, which consists of the harmonic balance method (HBM), arc-length continuation, and Hill’s method, is then adopted to compute periodic solution branches. Results show that once the excitation amplitude reaches some extent and the nonlinear stiffness of the resonator plays a dominant role due to higher response, only the nonlinear model can capture the dynamics of the coupling system. Furthermore, in the case of large responses, double peaks in frequency response bend right, and the second peak is significantly suppressed. Meanwhile, the location and wave attenuation performance of the bandgap remains unchanged. The results indicate that the nonlinear metamaterial beam performs better in the range out of bandgap. Hence, the nonlinear metamaterial is more robust against mistuning. Due to the above merit, the operating range of HSLDS resonators and the bearable excitation amplitude in nonlinear metamaterial beam are enhanced four times compared to linear metamaterial beam. Thus, the metamaterial beam with nonlinear HSLDS resonators has better environmental adaptability and broader application prospects.
... Liu [10] first clearly proposed the concept of LR structure in 2000 by periodically placing lead blocks wrapped in soft rubber in the polyurethane matrix, which demonstrates that the bandgap frequency is far lower than the Bragg scattering-induced bandgap frequency. Because of its potential for lowfrequency vibration control, LR structure has been studied by many scholars since it was proposed [11][12][13][14][15][16][17]. At present, the research on LR structures mainly focuses on broadening and lowering the bandgaps. ...
In order to suppress the transverse vibration of a plate, a quasi-zero-stiffness (QZS) resonator with tunable ultralow frequency bandgaps was introduced and analyzed. The resonator was designed by introducing the quasi-zero-stiffness systems into mass-in-mass resonators. The plane wave expansion method was employed to derive the bandgap characteristics of the locally resonant (LR) plate with QZS resonators, and corresponding simulations were carried out by finite element method (FEM). The results show that an LR plate with a QZS resonator can provide two bandgaps, and the ranges of the bandgaps agree well with the vibration attenuation bands calculated by FEM. Owing to the introduction of the QZS system, the bandgaps can be easily transferred to a lower frequency or even an ultralow frequency. The damping of the QZS resonators can effectively broaden the vibration attenuation bands. In addition, the differentiated design of the bandgap frequencies can be realized to obtain broadband low-frequency transverse wave suppression performance. Finally, a mechanical structure design scheme was proposed in order to achieve flexible adjustment of the bandgap frequency, which significantly increases the engineering applicability of QZS resonators.
... In periodic single beam investigations, Yu et al. [5] explored the characteristics of bending and propagating waves in elastic foundation-bound periodic beams, leading to the implementation of broadband absorption through multiple resonators attached to the beam [6]. Similarly, Patro et al. [7] conducted theoretical and experimental inquiries into cantilever beam structures with attached periodic cavity resonators. ...
This study presents a novel investigation into the phenomenon of coupled band gaps within double beam structures and achieves the construction of beam configurations featuring inherent coupled band gaps. Initially, the identification of coupled band gaps in double beam structures is discussed, and it is engineered within the low-frequency range by adjusting the thickness ratio of the two beams. Subsequently, double beam models are constructed using various methods. A comparative analysis between the Spectral Element Method and the Plane Wave Expand method validates the existence of coupled band gaps. Furthermore, through systematic exploration using the Plane Wave Expand method, we investigate the effect of different parameters on coupled band gaps. The attenuation properties within the identified coupled band gap are experimentally validated using double beam Finite Element models and a dedicated experiment for forced vibration testing. Consequently, controlled variations in thickness ratio confirm well-defined coupled band gaps exist in conventionally thick beam structures. Within this specific frequency range (254-279 Hz) for the double beam with thicknesses 0.01 m and 0.002 m, respectively, average attenuation rates of − 3.79 dB and − 11.16 dB are recorded correspondingly. It significantly contributes to applying theories on coupled band gaps to large-scale architectural frameworks.
... Increasing the number of resonators or targeting multiple resonance modes has also been proposed as an attempt to enlarge the attenuation bandwidth [54]. Hall et al. have explored this topic in detail both for single-layer [55] and multilayer [56] panel configurations. ...
Coupled resonances mechanisms combined with the notion of acoustic metamaterials offer exceptional sound
insulation capabilities, even at the challenging low frequency ranges below 1000 Hz. In this context, the
concept of Multiresonant Layered Acoustic Metamaterial (MLAM) emerged as a promising practical realization
exploiting this phenomenon to produce a double-peak sound transmission loss (STL) response in a multilayer
configuration that allows to overcome the challenge of manufacturing. This study proposes a novel enhanced
MLAM-based design (MLAM+) that greatly improves the device’s STL response by allowing the coupling of
a third additional peak, when compared to equivalent double-peak configurations. In contrast to existing
metamaterial-based solutions, this third peak is not caused by local resonance effects, but through inducing a
combined zero-stiffness response on the panel. Through analytical and numerical validation, it is demonstrated
that the frequency of this third peak can be controlled through the geometrical features of the layered design,
and it can be tuned to broaden the effective attenuation bandwidth and/or to increase the level of attenuation
without necessarily increasing the overall mass and maintaining the load-bearing capabilities of the panel. This
opens the path towards a metamaterial’s design methodology capable of tackling different functional outcomes
depending on the application
... Currently, vibration control primarily focuses on two aspects: passive suppression and active control [10,11], including damping vibration [12,13], vibration isolation [14], and dynamic absorbers [15], among others. Lazar et al [16] proposed a tuned inertial damper as an alternative to traditional dampers, which effectively suppresses cable vibration. ...
Carbon fiber pipe of the laser guiding arms are highly sensitive to vibration, and external vibrational excitation can significantly degrade the accuracy of the optical path. Firstly, this paper proposes a carbon fiber optical arm pipe magnetic support system for low-frequency and impulse vibrations. The overall stiffness of the magnetic support is reduced by the cooperation of mechanical springs with positive stiffness and magnetic springs with negative stiffness. Secondly, based on analytical calculations of magnetic forces and finite element simulations, a comprehensive dynamic model of the system is established and solved. Finally, an experimental platform for the equipment is set up, and both frequency sweep response tests and impulse vibration response tests are conducted on the system. The results demonstrate that the proposed magnetic support with low stiffness effectively reduces the interference of low-frequency vibrations on the supported carbon fiber pipe, and the vibration amplitude of the carbon fiber pipe has significantly decreased by 67%.
... The local resonance bandgap in metamaterial allows wave attenuation in the sub-wavelength scale [2], far outperforming conventional vibration/noise control solutions. By considering elaborately manufactured resonators, including but not limited to mass-spring chains [3][4][5][6][7], mass-membrane resonators [8][9][10], Helmholtz resonators [11,12], beam/plate-like resonators [13][14][15], a growing number of innovative designs for metamaterial have been proposed. The main limitation of these embodiments is the lack of tunability. ...
... The parameters in the tuning criterion (Eqs. (4),(5), and (11)) are, thereby, updated accordingly. It should be pointed out that using experimental results to correct the TBG or discarding the TBG and using experimentally based numerical bandgaps to guide the bandgap design are both relatively simple approaches. ...
... ,(5), or(11). The tuning strategy selection depends on the detected excitation type and is conducted by the microcontroller. ...
Programmable metamaterials for broadband vibration control draw growing interest due to their abilities to tailor dynamic responses. However, the deterministic dynamic behavior of any traditional metamaterial is a challenge to cope with the complex and variable vibration conditions in real environments. This work proposes an adaptive piezoelectric metamaterial beam (piezo-meta-beam) that consists of bimorph piezoelectric arrays. The shunt circuits are designed with self-tuning abilities by integrating microcontroller-driven digital potentiometers (POTs) into synthetic inductive circuits. Two typical scenarios are considered, i.e., harmonic and white noise excitations with different spectra. Different self-tuning strategies based on bandgap prediction are contrapuntally developed. However, a flaw in the analytical bandgap expression widely appearing in the literature is noted through a verification study. A modified bandgap expression based on the 3D finite element (FE) model is proposed for correction. This modified bandgap expression is adopted in formulating the control strategy of the microcontroller. A series of experiments are conducted to investigate the adaptive behavior of the piezo-meta-beam. In the harmonic sweep excitation test, the adaptive piezo-meta-beam shows an ultra-broad attenuation zone (220 – 720 Hz), while the traditional counterpart only has a bandgap width of less than 20 Hz. In the case of noise excitation, autonomous adjustment of the center frequency and attenuation zone is achieved for noises over different spectra. In general, this work presents a methodology for designing intelligent metamaterials that can adapt to environmental vibrations with vast potential for real applications.
... These properties limit the use of locally resonant metamaterials, where broadband wave suppression is desired. To this end, a few researchers started to consider the metamaterial structures with multiple resonators [35][36][37][38]. These structures can form multiple locally resonant band gaps to widen wave attenuation range. ...
... In recent years, the studies on the locally resonant (LR) metamaterials and metastructures [7][8][9][10] have provided new opportunities for structural vibration suppression and isolation owing to their unique attention has been aimed at the improvement or optimization of linear metastructure to achieve broadband structural vibration suppression with minimal weight addition. Several bandgap broadening approaches are proposed to improve the linear bandgap frequency regions, for example, using the multi-frequency resonators [23][24][25][26], forming the coupled bandgap [27,28], and introducing the active smart materials, such as shunted piezoelectric patches [29,30] and magnetorheological materials [31]. To solve the contradiction between the lightweight and broadband vibration suppression properties is a key concern for many scientists, especially in the aeronautical and astronautical industries. ...
