Plate Resonator Research Articles

Scale-Dependent Generalized Thermoelastic Damping in Vibrations of Small-Sized Rectangular Plate Resonators by Considering Three-Dimensional Heat Conduction

Given that thermoelastic damping (TED) is one of the main causes of energy dissipation in miniaturized structures, calculation of its exact amount is of particular importance in the design of such elements. Considering three-dimensional (3D) heat transfer along with the scale effect on both mechanical and thermal areas is one of the decisive factors in the more rigorous modeling of TED in small-sized resonators. This paper exploits the modified couple stress theory (MCST) and dual-phase-lag (DPL) heat conduction model to establish an analytical TED relation for rectangular micro/nanoplate resonators with 3D heat conduction. At the start, the non-Fourier heat equation corresponding to 3D DPL model is derived. Then, the solution of temperature distribution is determined by employing infinite trigonometric series. Moreover, the scale-dependent frequency of the system is presented in the context of MCST. Eventually, with the help of entropy generation (EG) method, an analytical TED expression considering 3D heat conduction is established. The precision of the presented solution is examined by comparing it with a simpler model available in the literature. By choosing two common types of boundary conditions, i.e. fully-clamped (CCCC) and fully-simply (SSSS) supported plates, the influence of various factors on TED changes is comprehensively investigated in simulation section. According to the outcomes, in plates with a lower ratio of length and width to thickness, the dimension considered for heat conduction model has a noticeable impact on the variations of TED.

Band gaps and dynamics of locally resonant meta-plate with stiffness adjustable low frequency resonator

This paper presents the band gaps and dynamics of locally resonant meta-plate with stiffness micro-adjustable high static and low dynamic resonator, in which a Euler-buckled beam provides negative stiffness. The resonator is periodically installed on a thin plate through a threaded linkage. By changing the axial displacement of the buckled beam, the total stiffness of the resonator is adjusted. Through the static analysis, the critical axial compression required for the buckled beam to provide negative stiffness is discussed. With the help of classical thin plate theory, the dynamic equation of the system is obtained. The band gaps of the locally resonant meta-plate are calculated by employing the plane wave expansion method. Considering the simply supported boundary condition, dynamic responses of the finite size locally resonant plate are shown with the aid of numerical simulation. The effects of the axial compression of the buckled beam, the mass of resonator, the damping of oscillators and plates, and spring stiffness of the system on the band gap are analyzed in detail.

Inertial amplification plates for low-frequency sound and vibration reduction

Reduction of vibration and sound radiation in the low-frequency range is a challenging task. In this work, a lever-type inertial amplification (LIA) mechanism is proposed to enhance the vibration reduction capability of thin plates. The mechanism consists of a rigid lever hinged on the host plate at two separate locations and a small mass mounted at the end of the lever. Band-structures of the unit cell and vibration transmissibility of the finite LIA plate are computed using the finite element method. Numerical results show that compared with the local resonant (LR) plates with the same added mass, the proposed LIA plates generate wider and deeper complete bandgaps at the same target frequency. The Bragg bandgaps occurring at higher frequencies are also broader compared with those of the LR plates due to a stronger impedance mismatch between the host plate and the attachments. Moreover, the vibration reduction performance of the LIA plate presents unique direction-dependent characteristics: maximum vibration attenuation is achieved when the LIA mechanisms are installed parallel to the wave propagation direction.

Acoustic rotation of multiple subwavelength cylinders for three-dimensional topography reconstruction

Accurate rotation of microparticles is of great significance in micro-rotors, multi-angle microscopic observation, microbial three-dimensional phenotyping, and microsystem assembly. However, most methods can only rotate a single object, thus limiting the throughput. In this study, we realized the simultaneous rotation of many trapped and aligned subwavelength glass cylinders inside an evanescent wave field excited by a resonant phononic crystal plate. The unique feature of the rotation lies in its periodic distribution as well as the rotation axis being perpendicular to the acoustic axis. The rotary power originates from viscous torque generated by the evanescent wave-induced near-boundary acoustic streaming's asymmetry distribution on the trapped cylinder. Furthermore, the three-dimensional topographies of rotated cylinders can be reconstructed from the microscopic images under different rotating angles. Our findings can pave the way toward developing simple, disposable, and scalable microfluidic devices for massive subwavelength acoustic rotation by carefully designing acoustic metamaterials.

Lightweight sound insulation optimization of simply supported locally resonant plate

A theoretical model of the normal sound insulation of a rectangular locally resonant (LR) plate with simply supported boundary conditions is established. The accuracy of the model is verified through comparison with finite element simulation results. Considering a 1-m2 aluminum plate as the research object, a non-dominated genetic algorithm is introduced. The algorithm optimizes the lightweight sound insulation of an LR finite plate with a center frequency band of 20–800 Hz as the optimization objective of maximum average sound insulation and minimum mass. The optimization parameters are substrate thickness and local resonance parameters (including resonator target frequency (fobj), number of resonators, additional mass ratio, and resonator damping). Optimization results indicate that the average sound insulation fluctuates at approximately 2 dB due to changes in fobj. The results also provide an optimal solution to the algorithm. The optimal sound insulation value curve of LR plates corresponding to different surface densities of intermediate improved cases is fitted and compared with the sound insulation value of an equal-mass bare plate. Under lightweight optimization, the resonators are deemed capable of improving the local frequency band sound insulation. In contrast, the wideband average sound insulation can approximate but not surpass the insulation provided by the equal-mass bare plate. In practical applications, an LR plate that can improve the local frequency band sound insulation and ensure the overall lightweight sound insulation performance of the wide frequency band can be obtained. This can be achieved by analyzing the frequency spectrum of optimal points in the lightweight sound insulation optimization process. Relevant research can provide a basis for the evaluation and design of the low-frequency sound insulation of plates for transportation equipment, such as airplanes, high-speed trains, and cars.

Development of an impact based pyroshock test setup using finite element and response surface methods

In this study, a simulation and test-based procedure is created and applied to develop mechanical pyroshock test setup. In order to build an effective design, preliminary input parameters are defined with finite element simulations. The agreement between impact simulations and experimental data was achieved for resonant plate, metallic anvil plate and gun system. The obtained Shock Response Spectrum (SRS) curves are not well fitted to explicit finite element simulations for nonmetallic anvil plate materials, such as felt, which also have significant contribution to results. Therefore, further improvement is established by using test-based Response Surface Method (RSM). After validating the relationship statistically, response optimizer was used to find the best combination of design parameters to achieve target SRS curve. Finally, the prediction was checked experimentally to show the effectiveness of the developed methodology.

Nonlinear vibrations of auxetic honeycomb thin plates based on the modified Gibson functions

Auxetic honeycombs possess many excellent properties, making them ideal cores for sandwich structures that can absorb energy effectively. This paper investigates the nonlinear vibrations of auxetic honeycomb composite plates, focusing on the primary resonance, super-/sub-harmonic resonances of the composite plates. Two pure panels sandwich an auxetic honeycomb core to form the honeycomb composite plate. The proposed modified Gibson function enables the derivation of effective material properties. By considering geometric nonlinearity, the nonlinear motion equations are derived through the implementation of the Hamilton principle, and then nonlinear ordinary differential equations are given by introducing stress functions and the Galerkin method. The nonlinear response curves are then determined by the multiple scale method. The impact of important parameters on the nonlinear vibration of auxetic honeycomb composite plates is evaluated in this study.

Active band gap control of magnetorheological meta-plate using frequency feedback control law

An innovative special class of magnetorheological metamaterial is proposed to achieve a tunable band gap using a new frequency feedback control law. By using the frequency feedback control law, the active band gap can intelligently track the external excitation frequency. The active control function of the band gap is realized using an intelligent local resonator embedded in the plate. Such a local resonator consists of a mass and a magnetorheological elastomer (MRE) driven by an external magnetic field. The local resonator and metamaterial plate are modeled analytically, and an analytical expression is derived to predict the band gap region. The effect of the external magnetic field on vibration attenuations is analyzed by the Galerkin method. Subsequently, a closed-loop frequency feedback control strategy is used to actively adjust the band gap according to the excitation frequency. Based on this frequency feedback control strategy, the effective band gap range of the metamaterial plate can be largely widened. The effect of damping of the MRE on broadband vibration reduction is also investigated, and the results show that the damping of the MRE plays an important role in the control of the band gap of the magnetorheological metamaterial.

Broadband low-frequency sound insulation of a metamaterial plate with inertial amplification

The recent development of Inertia Amplification (IA) acoustic metamaterial (AMM) opens a new venue for insulating low-frequency sound waves. This differs from conventional approaches that rely excessively on the structural density of the insulator and, therefore, lead to prohibitively heavy structures. The IA-AMM acquires a large effective density and a broad flexural bandgap by amplifying the inertia of many small mass elements periodically distributed in its unit cells, thus holding great promise as an effective yet lightweight solution for low-frequency sound insulation. This paper explores this possibility through numerical and experimental investigations. A semi-analytical model of an IA-AMM plate is developed by combining analytical equations characterizing the kinematics of an IA mechanism and FEM equations governing the vibration of the host plate. Based on this model, sound transmission characteristics of the plate under various sound incidences are analyzed with different amplification angles. By comparing with a locally resonant AMM plate, we found that the IA-AMM plate's sound transmission losses (STLs) are significantly and systematically improved over a wide frequency range of 116–544 Hz. To understand the underlying physics, the band diagram of the IA-AMM plate is calculated, which indicates the formation of a flexural bandgap covering the frequencies of the improved STL. The velocity contour of the plate at the center frequency of this bandgap also reveals much-suppressed vibration velocity amplitudes and a dipole-like sound radiation directivity, further explaining the observed enhancement of the sound insulation ability. Numerically predicted improvement of sound insulation is finally confirmed by experiments.

Lever-type inertial amplification plates for low-frequency vibration reduction

In this work, a lever-type inertial amplification (LIA) metastructure is proposed to enhance the vibration reduction capability of thin plates in the low-frequency range. The mechanism consists of a rigid lever hinged on the host plate at two separate locations and a small mass mounted at the end of the lever. Band-structures of the unit cell and vibration transmissibility of the finite LIA plate are computed by using the combination of analytical method and finite element method. Numerical results show that compared with the local resonant (LR) plates with the same added mass, the proposed LIA plates generate wider and deeper complete bandgaps at the same target frequency. The Bragg bandgaps occurring at higher frequencies are also broader compared with those of the LR plates due to a stronger impedance mismatch between the host plate and the attachments. Moreover, the vibration reduction performance of the LIA plate presents unique direction-dependent characteristics: maximum vibration attenuation is achieved when the LIA mechanisms are installed parallel to the wave propagation direction. To address the issue that single-level LIA takes up too much space to install, a multi-level LIA design is proposed. On one hand, the multi-level design makes the LIA mechanisms much more compact without hampering their vibration reduction performance; on the other hand, the combination of sub-levels greatly enhances the design flexibility of LIA mechanisms. Finally, experiments are performed to further confirm the vibration reduction performance of the proposed LIA plates.

Determination of optimal combination of pumping and probing inputs in vibro-acoustic modulation for sensitive BVID detection of CFRP

In this work, the potential of using defect resonance-based vibro-acoustic modulation (VAM) spectroscopy to determine pumping and probing frequencies to maximize the nonlinear VAM response of carbon fiber reinforced polymer (CFRP) plates is investigated. An integrated 3D finite element (FE) model which implements the barely visible impact damage (BVID) due to impact force and the loading of ultrasonic signals is proposed. Based on this model, the scaling subtraction method (SSM) is used to determine the low-frequency global plate resonance that leading strongest defect excitation for pumping input (GPRpump) and high-frequency local defect resonance for probing input (LDRprobe). A scanning laser Doppler vibrometer (SLDV) is adopted to experimentally validated the proposed numerical methodology. Then, the maximum response amplitude (MRA) of nonlinear VAM response is proposed to evaluate the influence of defect resonance on the nonlinear VAM response. The numerical and experimental results are in good agreement and show that MRA of the VAM sideband can be improved when the GPRpump frequency is taken as the pumping input and the LDRprobe frequency is taken as the probing input, respectively. The best BVID detection effect is obtained when the pumping input of the VAM test is selected as the GPRpump frequency and the probing input is selected as sum or difference of the GPRpump frequency and LDRprobe frequency.

A Power-Based Framework for Quantifying Parameter Uncertainties in Finite Vibroacoustic Metamaterial Plates.

Vibroacoustic metamaterials (VAMMs) are artificial materials that are specifically designed to control, direct, and manipulate sound waves by creating a frequency gap, known as the stop band, which blocks free wave propagation. In this paper, a new power-based approach that relies on the active structural intensity (STI) for predicting the stop band behavior of finite VAMM structures is presented. The proposed method quantifies the power loss in a locally resonant finite VAMM plate in terms of percentage, such as STI99% and STI90%, for stop band prediction. This allows for the quantitative analysis of the vibration attenuation capabilities of a VAMM structure. This study is presented in the context of a two-dimensional VAMM plate with 25 resonators mounted in the middle section of the plate. It has been demonstrated that this method can predict the stop band limits of a finite VAMM plate more accurately than using negative effective mass, unit cell dispersion analysis, or the frequency response function methods. The proposed approach is then implemented to establish a framework for investigating the influence of parameter uncertainties on the stop band behavior of the VAMM plate. Based on the STI99% method, which aims for significant vibration reduction, stricter tolerances in the mass fabrication process are required to ensure the robustness of VAMM. Conversely, the STI90% method suggests that larger fabrication tolerances can be leveraged to achieve a broader stop band range while still meeting the desired performance level, leading to cost savings in manufacturing.

On pyroshock tests for aerospace equipment qualification: A comprehensive parametric model for the simulation and the design of pyroshock test facilities

Spacecraft and related onboard equipment are subject to strong dynamic loads during the different phases of the missions. In particular, severe high-frequency shocks - mainly caused by the activation of pyrotechnic devices (hence the name "pyroshock") - are transmitted to the entire structure and could cause mission failure and safety-critical damages. Therefore, the verification tests of the aerospace equipment are essential to prove the resistance of the instrumentation to impulsive loads. The requirements for this qualification are usually expressed in terms of Shock Response Spectrum (SRS) acceleration and different launch vehicles cause different SRS. Therefore, the laboratory tests have the objective of simulating the real shock load conditions and - at the same time - being repeatable and safe. For these reasons, the most common test facilities exploit the launch of an impacting object (e.g., hammers or bullets) on resonant plates, interposed supporting the component under test. Recently, many studies have focused attention on the development of numerical analyses to predict the shock responses of these structures, given that their calibration is currently conducted with empirical techniques and involves considerable costs and downtime. This work aims to present an effective parametric model both for the simulation of pyroshock tests and for the optimization of the design of test facilities. The novel implementation of an embedded Computer-Aided Design (CAD) modeler – integrated with a Finite Element (FE) solver – and a Genetic Algorithm (GA) optimizer makes the proposed model both accurate and flexible. Precisely its flexibility makes it possible to effortlessly and efficiently satisfy the variable SRS requirements, reducing calibration times and - consequently - entailing remarkable economic advantages. The proposed model is developed entirely in the frequency domain, making it accurate and fast in computational terms. Furthermore, a comparison between the simulated pulse and a real force profile obtained from an impact characterization is presented.

Subwavelength path-switchable wave routing and topological corner states for a higher-order topological insulator

Wave manipulation has always been popular research subject due to its striking physical phenomena and promising real-life engineering applications. Recently, the birth of topological insulators carved a new way for wave control because of the capabilities of such insulators in confining wave propagation along specific directions. However, routing such wave guiding path with a flexible approach and further exploration about higher-order topological insulators are still very immature. In this regard, we wish to tackle this issue by introducing anisotropy into a local resonance plate with C4v symmetry. Through comprehensive theoretical and numerical research, we reveal the whole picture of bandgaps and topological properties by tuning the distance between resonators. Distinct topological edge states along different directions can be enabled by purposely designing anisotropy and controlling phase confliction. Based on this phenomenon, a path-switchable wave-guiding topological insulator is designed where the wave transmission path can be flexibly tuned by changing the operating frequency. Subsequently, we design a higher-order topological insulator which exhibits remarkable energy concentration at corners due to the topological corner states. Regarding these properties, our research provides an eligible candidate for achieving wave filtering, wave routing, and we also offer possible solutions for next generation integrated solid-state phononic circuits.

Structure-borne noise of steel and concrete box girders in an urban metro system: A hybrid evaluation and parametric study

Metro systems provide an efficient, convenient, and expeditious way to travel around crowded routes. Because these systems are established in cities, residential buildings close to metro viaducts are significantly affected by structure-borne noise (SBN). Although most previous studies developed SBN prediction with a focus on the accuracy and computational efficiency of a specific bridge type, only limited studies on parameters for the SBN on bridges were carried out. Thus, eliminating SBN is still a challenging task for both the design and operation phases of bridge design. Therefore, this study integrates simplified experiments with numerical analyses to evaluate the influential parameters on the structure-borne noise level (SBNL) for two types of bridge girders, that is, the double-box pre-stressed concrete girder and the double-box steel girder. The present study also proposes an optimization method for reducing the SBNL in the bridge design and operation phases and identifies the sources of SBN for these two types of bridges. In this paper, the solutions to mitigating SBN are first reviewed and briefly introduced. Theories associated with SBN are then derived and experimentally verified using a concrete or steel plate with a unit area. A hybrid evaluation method is developed to integrate transient finite-element simulation with experimental results, and the main sources (e.g., plate thickness, train speed, fastener stiffness, and track irregularity) that induce SBN are examined by this hybrid method. Consequently, the approach to resolving the SBN problem can be optimally determined. As demonstrated in the results from the hybrid evaluation method, the track condition dominates the SBNL for both types of bridges, and the relationship between train speed and plate eigenfrequency should be carefully investigated to avoid the effect of plate resonance. The pre-stressed concrete box girder is the recommended bridge type for use in urban areas from the viewpoint of minimizing the SBNL.

Self-Excited-Resonance of Soil-Engaging Surface Spectrum: A New Method of Soil Cutting Resistance Reduction

In this study we explored the methods and effects of spectral resistance reduction for soil-engaging surface of self-excited resonant bulldozing plates with a plane base on the basis of resonance effects. In the acquisition of the low-order vibration frequency f0 of the bin soil, centering around frequency point f0, eight spatial geometric wave frequency points ni of soil-engaging surfaces and three amplitudes were selected; by superimposing with soil-engaging surfaces of plane-based bulldozing plates, 24 spectral structures of the soil-engaging surface of bulldozing plates and model samples were combinatorically designed. Resistance reduction characteristics of each model sample were tested using an indoor soil bin test. Near the resonance point f0, the structures of the self-excited vibrating frequency spectrum of the soil-engaging surface obtain a preferable inhibitory effect on working resistance. At a 4 mm amplitude resonance point, model samples achieved the best resistance reduction effect, with a maximum relative resistance reduction rate of 22.67%, and the soil desorption effect of the relevant model sample was also good. On the other hand, away from the resonance point, whether the frequency increased or decreased, the corresponding working resistance of the model sample surfaces increased relatively. This is in good agreement with the law that the resonance point amplitude of the theoretical resonance curve is higher and the amplitude on both sides is lower. This paper provides a reference for the parameter design and related product development for various forced or self-excited vibration soil cutting tools.

Vibro-Acoustic Performance of a Fluid-Loaded Periodic Locally Resonant Plate

The vibro-acoustic performance of a fluid-loaded periodic locally resonant (LR) plate was examined in this research, with a specific focus on the effect of water fluid on the vibration and sound radiation of the LR structure. The analytical models of the fluid-loaded LR plate’s band gap, vibration, and acoustic radiation were theoretically derived with closed-form solutions, which can be used to predict the general vibro-acoustic rules of underwater LR structure. The results show that the LR band-gap width and Bragg frequency are significantly reduced when water fluid is considered. Besides, the frequency range that can be tuned to control the vibration and sound radiation for the LR plate with fluid is much narrower than that without fluid. The reason for inducing the above effects was also given in this research, which can be physically explained by the attached mass caused by the water fluid. In addition, the reason for the enhanced radiation efficiency close above the band gap was also discussed, which is caused by the change of radiation mode from corner or edge radiation to monopole radiation. Furthermore, adding small damping into the resonator could reduce the vibration and sound radiation in the frequency range above or close below the band gap, inducing the attenuation zone to be significantly broadened. Thus, designing the periodic resonators with proper damping could be an efficient method to make the LR plate more beneficial for vibration and noise reduction in water-surrounding applications.

The gas-liquid-Q-factor-inversion in MEMS plate resonators

We present a semi-numerical method for solving the dynamics of microplates in viscous fluids. The method is based on the Kirchhoff plate equation with a hydrodynamic force deduced from the Stokes equations. The equation of motion is solved with the Galerkin mode decomposition (GMD) using the vacuum vibrational modes of cantilevered microplates as the basis functions. We investigate the Q-factor of the vibrational modes of microplate-resonators in gases and liquids. In gases, the Euler–Bernoulli (EB) modes (modes with nodal lines only along the plate’s width) exhibit the lowest Q-factors, while non-EB modes exhibit the highest Q-factors. In liquids, the opposite is found. EB modes exhibit the highest Q-factors, and non-EB modes lower Q-factors. We name this opposite Q-factor pattern in gases and liquids the gas-liquid-Q-inversion (GL-Q-inversion). Experiments in water and air showed a Q-factor agreement with the GL-Q-inversion, and differences in Q-factor between simulation and experiments were below 25%. Further numerical analysis reveals the physical mechanism underlying the GL-Q-inversion in terms of the system’s stored and dissipated energy. The results and methods shown here will pave the way to efficiently exploit the two-dimensional vibrational modes of microplate-resonators to improve their performance in gaseous and liquid environments.

Visualization of rainbow trapping effect in higher-order topological insulators

The rainbow trapping effect, which enables field amplification of multiple wavelengths in topological insulators, offers unprecedented opportunities for integrated ultrasonic sensors and energy harvesting. However, until now, the realization of the rainbow trapping effect has been limited to a one-dimensional (1D) or 2D interface in the electromagnetic and acoustic systems. Here, we propose a method to realize rainbow trapping based on higher-order topological corner modes (HOTCMs), where the elastic wave is localized at 0D corners rather than at the interface. We strategically design the two-dimensional elastic locally resonant metamaterial plate and construct multiple HOTCMs at the interfacial corners formed by trivial and nontrivial domains. We further investigate the interplay between nearest-neighbor couplings and next-nearest-neighbor couplings. Remarkably, the HOTCMs localized at corners with different geometric configurations are shown to be frequency dependent, providing a platform for trapping elastic waves at different corners. Moreover, we demonstrate rainbow trapping based on the HOTCMs at the corners and show the agreement between the experimental results and theoretical modeling. Our results provide a mechanism to realize the trapping of multiple frequencies and extend the use of elastic integrated devices toward higher order topological insulators.

Analysis and characterization of structural, dielectric and magnetic properties of MgxCo(0.90−x)Zn0.10Fe2O4 nanoparticles based flexible metamaterial absorber for wireless communication

The anisotropic flexible metamaterial absorber (FMA) structure comprises a resonating layer, a ferrite-based flexible substrate layer, and a back layer. The sol-gel method is used to prepare the ferrite-based nanomaterial for enhancing absorbability. The solution prepared material is according to the formula of MgxCo(0.90−x)Zn0.10Fe2O4 and specified as X25, X50, X75 for X = 25%, 50%, and 75%, respectively. Then the proposed ferrites materials are characterized by XRD, and FESEM, respectively. Moreover, the magnetic and dielectric properties of the proposed MgxCo(0.90−x)Zn0.10Fe2O4 ferrites samples were explored for microwave applications. The dielectric constants and loss tangents of the fabricated, flexible substrates are measured at a frequency range of 3–7 GHz using the DAK 3.5. The computed relative permittivity values are 2.95 for X25, 3.55 for X50, and 4.05 for X75, respectively, while the loss tangents values are 0.00295 for X25, 0.00495 for X50, and 0.00695 for X75. Whereas the permeability and magnetic loss tangent values varied from 0.875 to 1.00 and 0.00225–0.00585, respectively. Finally, the resonators of the absorber consist of a Y-style shape, square-shaped metallic plate resonator, square ring resonator (SRR), and cross-liked shape. The proposed flexible metamaterial absorber (FMA) structure is developed on MgxCo(0.90−x)Zn0.10Fe2O4 nanomaterial-based flexible substrate with dimensions of 0.110λ x 0.110λ x 0.017λ to validate the design experimentally. The electrical dimension is calculated at a 5.5 GHz resonance frequency. The simulated results from the CST Microwave Studio simulator reveal that absorption peaks at 5.5 GHz with a 99.99% absorption that includes the C band frequency that can be used in satellite applications. The proposed FMA structure achieved a 60° incident angle response for TE and TM modes. The structure has superiority with compact dimensions, lightweight, and flexibility and can be used for C band wireless communications.