Plate Resonator Research Articles

Nonlinear combined resonance of magneto-electro-elastic plates

The existing articles on the nonlinear resonances of magneto-electro-elastic (MEE) structures are mainly devoted to the parametric resonance and primary resonance, neglecting the coupling effect between parametric and forced excitations. To reveal this issue, the coupled longitudinal and transverse excitations are considered to investigate the combined resonance of MEE plates, in which the simply supported ends is considered. The expressions of magnetic-, electric- and displacement-fields are determined using the Maxwell's equation and first order shear deformation theory (FSDT). Applying the Galerkin method, the nonlinear ordinary differential equations are derived. The combined resonance problem of MEE plates with simply supported ends is solved by developing the method of varying amplitude (MVA). And the resonance trajectory is depicted by amplitude-frequency diagram in the follow-up analysis, in which the complicated dynamical phenomena with jump, hysteresis and multi-stable solution can be observed. To reveal the dynamic mechanism, comprehensive numerical analyses including electric potential, magnetic potential, excitations, temperature variation and other factors are conducted, the bifurcation and chaotic dynamic behaviors are also analyzed. The results elucidate that these parameters under discussion play significant roles.

Characterization of pore water distribution in unsaturated soils during drying process with NMR and soil-water characteristic curves

The soil–water characteristic curve, which illustrates the relationship between water content and matric suction, is crucial for both unsaturated soil theory and engineering applications. Since water content significantly affects unsaturated soil strength, experimentally examine the distribution of water within the soil matrix. First, three types of soil are prepared for nuclear magnetic resonance and pressure plate tests, conducted over a range of matric suctions from 0 to 1400 kPa. Then, the pressure plate testreveals that matric suction expels free water first, leaving bound water, which remains until reaching critical suction point. NMR test is also performed to analyze the dynamics of pore water distribution during drying process. As matric suction increases, the peak of signal amplitude decreases, shifting leftward, reflecting water drainage from larger to smaller pores. In addition, two drainage stages are identified, considering distinct ranges of matric suction. Large pores drain more quickly, while smaller pores retain water for a longer period, challenging simpler models of pore drainage. The dynamic distribution of pore water reveals the evolution of water expulsion from the soil over time. This sheds light on water distribution and drainage behavior, emphasizing the need for advanced models that account for pore connectivity and water retention mechanisms.

Overdamping of vibration resonances by liquid crystal elastomers

This work aims to compare the capability of vibration attenuation by standard elastomeric polymers, and by the new anomalously damping nematic liquid crystal elastomer. We use the most mainstream materials in both categories, and design two testing platforms: the ASTM-standard constrained layer plate resonance geometry, and the attenuation of resonances in a commercial device (electric drill) where the damping polymers were inserted into the casing. In the standard plate resonance testing, we find that LCE outperforms all standard damping materials, moreover, it brings the vibrating plate into the overdamped condition, which is unique for a non-fluid dissipative system. In the attenuation of high-frequency vibrations of a device, we also found LCE dissipates these vibrations much better, although we did not find the optimal insertion configuration for the damping polymer, and did not reach overdamping.

Deep subwavelength sound absorption by a buckling plate resonator

Conventional sound-absorbing materials face great difficulties in achieving deep subwavelength broadband sound absorption due to the causal constraint on the minimum thickness. A buckling plate resonator is proposed to alleviate the causal constraint on the thickness of sound-absorbing materials. The resonator consists of a back cavity sealed by an elastic circular thin plate. When the plate is subjected to a uniform in-plane compressive force up to its critical load, it buckles and behaves as a negative stiffness spring. The positive stiffness of the back cavity is counteracted by the negative stiffness of the buckling plate, resulting in resonance absorption at the deep subwavelength scale. The sound absorption performance of the buckling plate resonator under different in-plane loads was measured in an impedance tube. Quasi-perfect sound absorption was observed in a buckling plate resonator with a thickness less than 1% of the wavelength corresponding to the resonance frequency. This work provides a solution for the design of ultra-thin broadband sound absorbers.

Dispersion and ellipticity of Rayleigh waves in a soil substrate supporting resonant beams and plates

Dispersion and ellipticity of Rayleigh waves in a soil substrate supporting resonant beams and plates

Thermoelastic damping in asymmetric vibrations of nonlocal circular plate resonators with Moore-Gibson-Thompson heat conduction

Precise estimation of the amount of thermoelastic damping (TED) in small-sized resonators is one of the crucial issues in their optimal design. According to several experimental, numerical and theoretical findings, the behavior of structures with such small dimensions in structural and thermal domains does not follow classical elasticity theory and the Fourier law of heat conduction. The objective of this work is to develop a nonclassical formulation for computing TED in asymmetric vibrations of circular nanoplates according to nonlocal theory (NT) and Moore-Gibson-Thompson (MGT) heat transfer model. To do so, first, the coupled equations of motion and heat are derived in the purview of NT and MGT model. Then, the real and imaginary parts of the system frequency are extracted from the frequency equation affected by thermoelastic coupling. Finally, by means of the existing definition for TED, a mathematical expression including nonlocal parameter of NT and nonclassical constants of MGT model is obtained to make an estimate of TED value. In the numerical examples section, to ensure the credibility of the provided formulation, the results obtained through this model are compared with those reported in the literature in the context of simpler models. Then, by presenting various graphical data, the type and extent of the role of different factors in TED changes are appraised. The obtained results indicate that employing NT and MGT model can substantially impact the amount of TED compared to the estimations of the classical formulation. Furthermore, the comparison of results reveals that the magnitude of TED in asymmetric vibration modes surpasses that in symmetric ones, and consequently incorporating asymmetric vibration modes is crucial for thorough analysis of TED in circular nanoplates. Thus, the formulation presented in this article can aid in achieving an optimal design for such plates, particularly in terms of minimizing energy loss.

Efficient and accurate analysis of locally resonant acoustic metamaterial plates using computational homogenization

Efficient and accurate analysis of locally resonant acoustic metamaterial plates using computational homogenization

Simultaneous laser ultrasonic measurement of sound velocities and thickness of plates using combined mode local acoustic spectroscopy

Standard ultrasonic thickness measurements require the sound velocity of the sample to be known and vice versa. We present a method, which we have termed combined mode local acoustic spectroscopy (CoMLAS) for simultaneously determining a plate’s thickness and sound velocities without requiring such a priori knowledge. It is based on a combination of three guided wave modes sustained by a plate at discrete frequencies, which we generate and detect using laser ultrasound. We use a pulsed laser that is shaped into a periodic line pattern on the sample’s surface to generate elastic waves and measure the response at the pattern’s center with a vibrometer. The surface acoustic wave mode produces an interference peak in the response spectrum at the frequency corresponding to the wavelength matching the pattern line spacing. By limiting the total size of the excitation pattern, we can simultaneously generate two zero-group-velocity plate resonances, providing two additional peaks in the spectrum. The plate’s local thickness and longitudinal and transverse sound velocities are calculated from the peak frequencies. We demonstrate the feasibility of CoMLAS on steel and aluminum sheets with a thickness of around 2mm by resolving thickness steps and temperature-induced changes in the sound velocities. Using numerical simulations and control experiments, we provide insights into the method’s accuracy and limitations. The choice of excitation pattern, the method’s sensitivity, and the influence of sample inhomogeneity and anisotropy are discussed. CoMLAS does not require scanning mechanics and provides local plate properties. The results shown are achieved with low-energy lasers and signal averaging. Considerations on signal-to-noise ratio indicate that a realization with available lasers of higher energy will enable single-shot measurements. This qualifies the method for use on moving samples in an industrial environment.

Low-Frequency Flexural Wave Acoustic Insulation Characteristics of a Double-Layer Metamaterial Plate

The effects of geometric parameters and constituent material parameters on the flexural wave bandgap of a locally resonant double-layer metamaterial plate are investigated using the finite element method. Reasonable parameters are obtained through optimization; then, a double-layer plate made of ABS material with added aluminum mass blocks is designed. The results show that it can open the low-frequency (112--124 Hz) flexural wave bandgap at a subwavelength size. The metamaterial plate is modeled as an equivalent spring-mass system, and the frequency range with negative density for the equivalent dynamic mass is consistent with the width of the flexural wave bandgap. The bandgap generation mechanism is further elucidated. Sound insulation performance of double-layer metamaterial panels verified in an acoustic chamber. The maximum amplitude of STL is achieved at the 112 Hz point in the bandgap frequency range, which indicates that the low-frequency bandgap can effectively reduce vibration and noise. These results demonstrate that this novel double-layer metamaterial plate has wide applications in engineering.

Vibration attenuation and wave propagation analysis of 3D star-shaped resonant plate structures and their derivatives with ultra-wide band gap

Based on the local resonance effect of elastic waves, three single-phase acoustic metamaterials are proposed in this paper. Based on the finite element method and Bloch's theorem, the energy band structure diagrams and vibration modes are plotted, and the band gap properties and band gap opening mechanism of these structures are explored. New structures possessing lower frequency band gaps are obtained by topological optimization. The transmission curves verify the accuracy of the band gap and the vibration attenuation ability of the structure. Finally, the structural parameters were adjusted and the effect of each parameter change on the band gap characteristics was analyzed. The results show that the proposed structure has a maximum band gap coverage of 72.4 % and a strongest attenuation peak of less than −400 (dB) due to the occurrence of a local resonance. This paper provides a methodology for analyzing the vibration and noise reduction performance of single-phase material phononic crystals, as well as a three-dimensional phononic crystal with potential for practical applications.

Low-frequency and broadband vibration absorption of a metamaterial plate with acoustic black hole resonators

Acoustic metamaterials with bandgap properties can lead to effective vibration attenuation in a targeted frequency range. In this paper, a novel locally resonant metamaterial plate is proposed, connected with acoustic black hole (ABH) resonators. The structure is shown to achieve low-frequency and broadband vibration absorption. The proposed microunit design consists of three parts: the ABH resonator, supporting beams as the connector, and the frame (FC-ABH). The modal characteristics of the microunit and the dispersion relation of the infinite periodic FC-ABH structure are calculated by both Gaussian expansion method and finite element method. By the effects of flexural wave absorption of ABH coupled with the local resonance mechanism, a low-frequency and broad vibration attenuation band can be generated. When the damping of materials is included, the attenuation band can be further widened, with relative bandwidth measured by the experiment up to 0.93. The results of numerical simulations and experimental tests demonstrate that the finite periodic FC-ABH can act as an effective vibration absorber and isolator. The proposed structure may provide new ideas for the design and application of broadband vibration mitigation metadevices.

Mechanisms of multi-bandgap inertial amplification applied in metamaterial sandwich plates

The design concept of integrating locally resonant metamaterials with sandwich plates has demonstrated promising prospects in the development of lightweight, load-bearing structures endowed with excellent capabilities for noise and vibration attenuation. However, achieving low-frequency vibration attenuation in the locally resonant metamaterial sandwich plates remains a challenging task that frequently requires the inclusion of additional centralized mass or heavy local resonators. This study proposes a novel multi-bandgap metamaterial sandwich plate with the lever-type inertial amplification mechanism (LIA-MMSP) for achieving the low-frequency vibration attenuation. Compared with the metamaterial sandwich plates incorporating multi-frequency local resonators (LR-MMSP) with equivalent additional mass, the LIA-MMSP exhibits the ability to achieve lower-frequency multiple bandgaps. The theoretical dynamic model is employed to elucidate the underlying mechanism behind the generation of multiple bandgaps at lower frequencies in the LIA-MMSP. The vibration attenuation performances of the LIA-MMSP are analyzed through both the finite element method and experiment study. The effect of various parameters on the vibration transmission characteristics of the LIA-MMSP is studied. The results show that the boundary frequencies of the LIA-MMSP are precisely one of the lever ratios of the LR-MMSP. By altering the lever ratio within the LIA-MMSP, precise fine-tuning and optimization of the low-frequency multiple bandgaps are achievable. When the attached mass is constrained, increasing the lever ratio enables the achievement of lower bandgaps. In addition, as the eigenfrequency of the primary lever-type IA resonator fp and secondary lever-type IA resonator fs decrease, both the first attenuation zone (AZ1) and the second attenuation zone (AZ2) of the LIA-MMSP shift towards lower frequencies. However, as fp decreases, the width of AZ1 expands, and the minimum accelerations within the AZs decrease even further. Moreover, a normalized comparison provides validation of the exceptional performance of the proposed LIA-MMSP in terms of lightweight design, as well as its ability to achieve low-frequency broadband vibration attenuation.

Multiple scattering of local nonlinear resonators on a thin plate

Developing nonlinear resonant metamaterial plates requires an effective wave simulation method to analyze the wave interactions between multiple nonlinear scatterers. The multiple scattering method has the advantages of high computational efficiency and closed-form displacement solutions in modeling the finitely periodic scatterer array. However, the multiple scattering method of nonlinear scatterers is absent in the available studies of plate structures. In this paper, a nonlinear multiple scattering approach is formulated and analyzed for thin plates with nonlinear resonant scatterers. The resonant scatterer consists of an inner plate with a local resonator modeled by the nonlinear mass-spring system. The motion equation of resonant scatterers is solved using the perturbation technology and wave expansion method. The T-matrix of the resonant scatterer of each order is then derived at the arbitrary harmonic frequency from continuous interfacial conditions of resonant scatterers. Finally, the multiple scattering is formulated for a finitely periodic array of resonant scatterers on a thin plate. Numerical simulations capture the scattering characteristics and stop-band formations of fundamental and second-harmonic waves. Furthermore, the finitely periodic array of nonlinear and linear resonant scatterers achieves the nonreciprocal transmission of flexural waves. These numerical results demonstrate the potential applications of the proposed method in designing metamaterial-based plates with complex transmission properties.

Geometrically engineered mass sensing CMOS-MEMS resonators for temperature compensation via folded anchors

We present, for the first time, a single-layer plate resonator with specific folded anchors capable of reducing the temperature coefficient of frequency (TCF) by two orders of magnitude compared to straight beams. Folded anchors provide differential strain through either compressive or tensile thermal stress depending on the anchor design and, in turn, allow for positive and negative temperature-induced frequency change components. With a nominal 2 MHz frequency, we experimentally report a frequency shift of 2500 ppm over a temperature span from 0ºC to 90ºC using an optimal anchor folding aspect ratio. The frequency-temperature curve exhibits a turnover point at 27ºC granting a unique opportunity to, in a future application, complement this passive strategy with an active micro-oven for negligible TCF. The proposed approach main advantage relies on its mechanical design-level implementation exploiting a geometrical engineering strategy than can be directly extended to other topologies. This technique reveals as particularly suited for ultra-sensitive mass sensing applications based on microelectromechanical systems (MEMS) resonators where single-layer resonators are optimal thanks to their minimum footprint, attaining minimum mass structures. Results demonstrate that adoption of the proposed folded anchors strategy decreases effectively the thermally induced frequency fluctuations within the system intrinsic noise level.

Low-frequency vibration and noise control in sandwiched composite locally resonant metamaterials-embedded plate structures

This study proposes a sandwiched composite locally resonant metamaterial (SLRM) system and SLRM-embedded plate structure (SLRMeP) to effectively control low-frequency vibrations and sound radiation. The wave control mechanism and configuration of the proposed system are more suitable and realistic to address practical low-frequency vibro-acoustic problems. A numerical model was proposed based on the material properties, unit dimensions, and mass ratios to determine the local resonance characteristics and bandgap formation. The experimental results on a full-scale SLRMeP measuring 3000 × 4200 × 210 mm confirmed the efficacy of the local resonance bandgap for controlling vibrations and sound radiation, achieving a 94.08% reduction in the acceleration response and a 15.13 dB reduction in the sound pressure level. Additionally, variations in mass ratio, achieved by altering the mass density or dimensions, yield distinct bandgap behaviors, offering strategies to enhance vibro-acoustic performance.

Low-frequency vibration reduction of an underwater metamaterial plate excited by a turbulent boundary layer

Flow-induced structural noise is an important component of hydrodynamic noise of underwater structures. Local resonance metamaterials are considered to have excellent performance and enormous potential in the field of low-frequency vibration and noise control. To verify its potential, the paper derived the underwater band gap of a lateral local resonance (LLR) plate through the plane wave expansion (PWE). Then, utilizing the modal superposition approach and Rayleigh integral technique, the vibro-acoustic response of a LLR plate under a turbulent boundary layer (TBL) excitation is obtained. Finite element certification is also conducted through an uncorrelated wall plane wave technique. Parametric study is conducted to analyse the factors which influence the control effects. The result shows that the plate exhibits excellent suppression performance for flow-induced vibration at band gap frequencies. The band gaps and suppression ranges generated by the underwater metamaterial plate, are dramatically narrowed due to the thick fluid load. The paper provides theoretical guidance for the control of flow-induced structural vibration and the application of acoustic metamaterials.

A thin-walled cavity structure with double-layer tapered scatterer locally resonant metamaterial plates for extreme low-frequency attenuation

Locally resonant acoustic metamaterials (LRAMs) are effective spatial frequency filters due to their local resonance system. However, they own narrow stopbands, charge additional weight on the primary system, and operate only at the adjusted frequency range. In this paper, a novel dual-target LRAM is proposed based on coupling the cavity and convex mechanisms, utilizing the benefits of both sound-barrier and sound-absorbing types of acoustic metamaterials. A combination of the cavity and convex structures is presented and investigated for the first time, which exploits both the reflection and absorption theories simultaneously to improve the sound attenuation performance of acoustic metamaterials. By arranging two-layer finite periodic of 5×5 proposed convex unit cells along x and y directions and separating them by an air cavity, a supercell named hybrid locally resonant acoustic metamaterials (HLRAM) baffle is designed. The band structures, transmission spectrum, and displacement vector fields are calculated employing the finite element method (FEM). In addition, vibration modes at the edges of stopbands are computed and carefully analyzed to determine the formation mechanism, mechanics/dynamic response, and dispersion features of stopbands. Meanwhile, sensitivity analyses have been conducted on the model to investigate the influence of material and geometry parameters on dispersion characteristics. Equivalent spring-mass analytic models are used to direct the modifications of structure and the adjustment of structural and material parameters in order to achieve a wide stopband with a low opening frequency. Thereby, the effective stiffness and mass values influencing the starting and cutoff frequencies are adjusted in a desirable manner. The results show that the structure can generate a wide stopband that covers the frequency range of 64.9-805.6Hz, allowing the structure to block incoming acoustic waves with 35.42dB root mean square of noise attenuation (RMSNA) the given frequency range (0-1kHz). This study indicates that the HLRAM has a preponderance among conventional techniques as we can manipulate dispersion characteristics and the sound transmission loss (STL) based on the desired sound reduction level and shift stopbands to the intended frequency range. This can be achieved by altering cavity size, material, or geometry parameters.

Damage imaging in plates by evaluating local entropy in guided wavefield data

This paper presents a new algorithm called broadband entropy-based two-stage damage imaging (BE2DI) for the detection and imaging of defects in multi-layer plates.The method differentiates defects from either local scattering phenomena of propagating Lamb waves or locally increased vibrational activity for stimulated global plate resonances by exploiting the higher vibrational activity of full-field broadband vibration signals at defective regions and the distinct spatial behavior of defects and artifacts. Using these features, first, a candidate damage map is constructed by means of iterative thresholding based on descriptive statistics of broadband data. Afterwards, an adaptive regional damage index based on local entropy is introduced, which utilizes operational deflection shapes to process previously identified candidate regions and subsequently reveal both shallow and deep defects. BE2DI can be seen as an automated local defect resonance identification approach in the case of shallow defects. Multiple plates having various defect types with different sizes and depths are investigated. Broadband chirp signals are used to excite the plates using low-power piezoelectric actuators, and vibrational data is registered by 3D scanning laser Doppler vibrometry. The obtained results quantitatively and qualitatively demonstrate that the proposed method can effectively detect different kinds of damage, regardless of being shallow or deep.

Tunable Ultralow-Frequency Bandgaps Based on Locally Resonant Plate with Quasi-Zero-Stiffness Resonators

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.

Topological localized modes in moiré lattices of bilayer elastic plates with resonators

We investigate the existence of higher order topological localized modes in moiré lattices of bilayer elastic plates. Each plate has a hexagonal array of discrete resonators and one of the plates is rotated at an angle (21.78∘) which results in a periodic moiré lattice with the smallest area. The two plates are then coupled by inter-layer springs at discrete locations where the top and bottom plate resonators coincide. Dispersion analysis using the plane wave expansion method reveals that a bandgap opens on adding the inter-layer springs. The corresponding topological index, namely fractional corner mode, for bands below the bandgap predicts the presence of corner localized modes in a finite structure. Numerical simulations of frequency response show localization at all corners, consistent with the theoretical predictions. The considered continuous elastic bilayered moiré structures opens opportunities for novel wave phenomena, with potential applications in tunable energy localization and vibration isolation.