Modal Analysis of Bandgap Formation for Vibration Attenuation in Locally Resonant Finite Beams

2016 ◽  
Author(s):  
Christopher Sugino ◽  
Stephen Leadenham ◽  
Massimo Ruzzene ◽  
Alper Erturk
Keyword(s):  
Boundary Conditions ◽  
Modal Analysis ◽  
Low Frequency ◽  
Optimal Number ◽  
Frequency Range ◽  
Design Guideline ◽  
Arbitrary Boundary ◽  
Low Frequency Vibration ◽  
Vibration Attenuation ◽  
Unit Cells

Metamaterials made from locally resonating arrays can exhibit attenuation bandgaps at wavelengths much longer than the lattice size, enabling low-frequency vibration attenuation. For an effective use of such locally resonant metamaterial concepts, it is required to bridge the gap between the dispersion characteristics and modal behavior of the host structure with its resonators. To this end, we develop a novel argument for bandgap formation in finite-length beams, relying on modal analysis and the assumption of infinitely many resonators. This assumption is analogous to the wave assumption of an infinitely long beam composed of unit cells, but gives additional analytical insight into the bandgap, and yields a simple formula for the frequency range of the bandgap. We present a design guideline to place the bandgap for a finite beam with arbitrary boundary conditions in a desired frequency range that depends only on the total mass ratio and natural frequency of the resonators. For a beam with a finite number of resonators and specified boundary conditions, we suggest a method for choosing the optimal number of resonators. We validate the model with both finite-element simulations and a simple experiment, and draw conclusions.

scholarly journals Modal analysis and demonstration of metastructure combining local resonators and an autonomous synchronized switch damping circuit

2022 ◽  
pp. 146134842110682
Author(s):  
Haruhiko Asanuma ◽  
Sumito Yamauchi
Keyword(s):  
Modal Analysis ◽  
Low Frequency ◽  
Coupled Analysis ◽  
Resonant Vibration ◽  
Power Sources ◽  
Low Frequency Vibration ◽  
Vibration Attenuation ◽  
Signal Processors ◽  
Coupled Equation ◽  
Frequency Axis

A locally resonant metastructure is a promising approach for low-frequency vibration attenuation, whereas the attachment of many resonators results in unnecessary and multiple resonance outside the bandgap. To address this issue, we propose a damping metastructure combining local resonators and an autonomous synchronized switch damping circuit. On the basis of modal analysis, we derive an electromechanically coupled equation of the proposed metastructure. The piezo ceramics, which are attached on a small portion of the metastructure and connected to the circuit, remarkably decrease the magnitude of the resonant vibration with no extra sensors, signal processors, or power sources. The displacement at unnecessary resonance was decreased by approximately 75%. The results of the coupled analysis were similar to the experimentally observed results in terms of the location and width of the bandgap on the frequency axis and the decreased displacement for the circuit. The proposed technique can overcome the disadvantage of the metastructure.

Electroelastic Bandgap Formation in Locally Resonant Metamaterial Beams With Piezoelectric Shunts: A Modal Analysis Approach

2016 ◽  
Author(s):  
Christopher Sugino ◽  
Stephen Leadenham ◽  
Massimo Ruzzene ◽  
Alper Erturk
Keyword(s):  
Modal Analysis ◽  
Flexible Structures ◽  
Design Guideline ◽  
Mechanical Metamaterials ◽  
Vibration Attenuation ◽  
Unit Cells ◽  
Modal Behavior ◽  
Resonant Shunt ◽  
Effective Design

Metamaterials made from flexible structures with piezoelectric laminates connected to resonant shunt circuits can exhibit vibration attenuation properties similar to those of their purely mechanical locally resonant counterparts. Thus, in analogy to purely mechanical metamaterials, electroelastic metamaterials with piezoelectric resonators can exhibit vibration attenuation bandgaps. To enable the effective design of these locally resonant electroelastic metamaterials, the electromechanical behavior of the piezoelectric patches must be reconciled with the modal behavior of the electroelastic structure. To this end, we develop a novel argument for the formation of bandgaps in bimorph piezoelectric beams, relying on modal analysis and the assumption of infinitely many segmented shunted electrodes (unit cells) on continuous piezoelectric laminates bracketing a substrate. As a case study, the frequency limits of the locally resonant bandgap that forms from resonant shunting is derived, and a design guideline is presented to place the bandgap in a desired frequency range. This method can be easily extended to more general circuit impedances, and can be used to design shunt circuits to obtain a desired frequency response in the main structure.

Vibration isolation characteristics of finite periodic tetra-chiral lattice coating filled with internal resonators

2016 ◽  
Vol 230 (16) ◽  
pp. 2840-2850 ◽  
Author(s):  
Dawei Zhu ◽  
Xiuchang Huang ◽  
Hongxing Hua ◽  
Hui Zheng
Keyword(s):  
Band Gap ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Band Gaps ◽  
Stiffened Plate ◽  
Frequency Range ◽  
Vibration Attenuation ◽  
Unit Cells ◽  
Internal Resonators

Owing to their locally resonant mechanism, internal resonators are usually used to provide band gaps in low-frequency region for many types of periodic structures. In this study, internal resonators are used to improve the vibration attenuation ability of finite periodic tetra-chiral coating, enabling high reduction of the radiated sound power by a vibrating stiffened plate. Based on the Bloch theorem and finite element method, the band gap characteristics of tetra-chiral unit cells filled with and without internal resonators are analysed and compared to reveal the relationship between band gaps and vibration modes of such tetra-chiral unit cells. The rotational vibration of internal resonators can effectively strengthen the vibration attenuation ability of tetra-chiral lattice and extend the effective frequency range of vibration attenuation. Two tetra-chiral lattices with and without internal resonators are respectively designed and their vibration transmissibilities are measured using the hammering method. The experimental results confirm the vibration isolation effect of the internal resonators on the finite periodic tetra-chiral lattice. The tetra-chiral lattice as an acoustic coating is applied to a stiffened plate, and analysis results indicate that the internal resonators can obviously enhance the vibration attenuation ability of tetra-chiral lattice coating in the frequency range of the band gap corresponding to the rotating vibration mode of internal resonators. When the soft rubber with the internal resonators in tetra-chiral layers has gradient elastic modulus, the vibration attenuation ability and noise reduction of the tetra-chiral lattice coating are basically enhanced in the frequency range of the corresponding band gaps of tetra-chiral unit cells.

Origami-Based Bistable Metastructures for Low-Frequency Vibration Control

2021 ◽  
Vol 88 (5) ◽  
Author(s):  
Mingkai Zhang ◽  
Jinkyu Yang ◽  
Rui Zhu
Keyword(s):  
Vibration Isolation ◽  
Energy Analysis ◽  
Geometrical Nonlinearity ◽  
Low Frequency ◽  
Quantitative Relationship ◽  
Vibration Modes ◽  
Two Dimensional ◽  
Low Frequency Vibration ◽  
Dynamic Experiments ◽  
Unit Cells

Abstract In this research, we aim to combine origami units with vibration-filtering metastructures. By employing the bistable origami structure as resonant unit cells, we propose metastructures with low-frequency vibration isolation ability. The geometrical nonlinearity of the origami building block is harnessed for the adjustable stiffness of the metastructure’s resonant unit. The quantitative relationship between the overall stiffness and geometric parameter of the origami unit is revealed through the potential energy analysis. Both static and dynamic experiments are conducted on the bistable origami cell and the constructed beam-like metastructure to verify the adjustable stiffness and the tunable vibration isolation zone, respectively. Finally, a two-dimensional (2D) plate-like metastructure is designed and numerically studied for the control of different vibration modes. The proposed origami-based metastructures can be potentially useful in various engineering applications where structures with vibration isolation abilities are appreciated.

scholarly journals Stiffness-based Spring Design Optimization using Taguchi Method to reduce Low-Frequency Vibration

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Ahmad Yusuf Ismail ◽  
Al Munawir ◽  
Noerpamoengkas A
Keyword(s):  
Taguchi Method ◽  
High Frequency ◽  
Vibration Isolation ◽  
Low Frequency ◽  
Stiffness Coefficient ◽  
Frequency Range ◽  
High Noise ◽  
Low Frequency Vibration ◽  
Optimization Variable ◽  
Vibration Transmissibility

Low-frequency vibration has been troublesome for a mechanical system. Despite the measurement difficulties, low-frequency vibration also creates several environmental effects such as high noise level that is harmful to the human body. One of the methods to reduce vibration is tuning the vibration isolation i.e. spring and damping coefficient. However, the latter method is found to be effective only for the mid-high frequency range. Therefore, this paper proposes an optimization of the spring a.k.a. stiffness coefficient in order to reduce the low-frequency vibration. The Taguchi method is used as an optimization tool since it offers simplicity yet powerful for any field of application, particularly in engineering. Two significant parameters in the spring geometry were selected as the optimization variable in the Taguchi method and evaluated using vibration transmissibility concept. The result shows that the Taguchi method has been successfully obtained the optimum value for the spring geometry purposely to reduce the vibration transmissibility.

A Hybrid Approach for the Modal Analysis of Continuous Systems With Localized Nonlinear Constraints

2010 ◽  
Author(s):  
M. R. Brake
Keyword(s):  
Boundary Conditions ◽  
Modal Analysis ◽  
Piecewise Linear ◽  
Hybrid Approach ◽  
Constitutive Relationship ◽  
Leaf Spring ◽  
Continuous Systems ◽  
Superposition Method ◽  
Arbitrary Boundary ◽  
Linear Force

The analysis of continuous systems with nonlinearities in their domain have previously been limited to either numerical approaches, or analytical methods that are constrained in the parameter space, boundary conditions, or order of the system. The present analysis develops a robust method for studying continuous systems with arbitrary boundary conditions and nonlinearities using the assumption that the nonlinear constraint can be modeled with a piecewise-linear force-deflection constitutive relationship. Under this assumption, a superposition method is used to generate homogeneous boundary conditions, and modal analysis is used to find the displacement of the system in each state of the piecewise-linear nonlinearity. In order to map across each nonlinearity in the piecewise-linear force-deflection profile, a variational calculus approach is taken that minimizes the L2 energy norm between the previous and current states. To illustrate this method, a leaf spring coupled with a connector pin immersed in a viscous fluid is modeled as a beam with a piecewise-linear constraint. From the results of the convergence and parameter studies, a high correlation between the finite-time Lyapunov exponents and the contact time per period of the excitation is observed. The parameter studies also indicate that when the system’s parameters are changed in order to reduce the magnitude of the velocity impact between the leaf spring and connector pin, the extent of the regions over which a chaotic response is observed increases.

Optimization of Viscoelastic Metamaterials for Vibration Attenuation Properties

2020 ◽  
pp. 2050116
Author(s):  
Ratiba F. Ghachi ◽  
Wael I. Alnahhal ◽  
Osama Abdeljaber ◽  
Jamil Renno ◽  
A. B. M. Tahidul Haque ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Experimental Testing ◽  
Low Frequency ◽  
Optimization Procedure ◽  
Bragg Scattering ◽  
Frequency Range ◽  
Element Analysis ◽  
Scattering Effect ◽  
Vibration Attenuation ◽  
Electrodynamic Shaker

Metamaterials (MMs) are composites that are artificially engineered to have unconventional mechanical properties that stem from their microstructural geometry rather than from their chemical composition. Several studies have shown the effectiveness of viscoelastic MMs in vibration attenuation due to their inherent vibration dissipation properties and the Bragg scattering effect. This study presents a multiobjective optimization based on genetic algorithms (GA) that aims to find a viscoelastic MM crystal with the highest vibration attenuation in a chosen low-frequency range. A multiobjective optimization allows considering the attenuation due to the MM inertia versus the Bragg scattering effect resulting from the periodicity of the MM. The investigated parameters that influence wave transmission in a one-dimensional (1D) MM crystal included the lattice constant, the number of cells and the layers’ thickness. Experimental testing and finite element analysis were used to support the optimization procedure. An electrodynamic shaker was used to measure the vibration transmission of the three control specimens and the optimal specimen in the frequency range 1–1200[Formula: see text]Hz. The test results demonstrated that the optimized specimen provides better vibration attenuation than the control specimens by both having a band-gap starting at a lower frequency and having less transmission at its passband.

scholarly journals Low-Frequency Vibration and Radiation Performance of a Locally Resonant Plate Attached with Periodic Multiple Resonators

2020 ◽  
Vol 10 (8) ◽  
pp. 2843
Author(s):  
Qi Qin ◽  
Meiping Sheng ◽  
Zhiwei Guo
Keyword(s):  
Boundary Conditions ◽  
Band Gap ◽  
Low Frequency ◽  
Expansion Method ◽  
Acoustic Power ◽  
Radiation Efficiency ◽  
Band Gaps ◽  
Periodic Arrays ◽  
Low Frequency Vibration ◽  
The One

The low-frequency vibration and radiation performance of a locally resonant (LR) plate with periodic multiple resonators is studied in this paper, with both infinite and finite structure properties examined. For the finite cases, taking the LR plate attached with two periodic arrays of resonators as an example, the forced vibration response and the radiation efficiency are theoretically derived by adopting a general model with elastic boundary conditions. Through a comparison with the band structures calculated by the plane-wave-expansion method, it shows that the band gaps in the infinite LR plate are in good agreement with the vibration-attenuation bands in the finite LR plate, no matter what boundary conditions are applied to the latter. In contrast to the vibration reduction in the band gaps, the radiation efficiency of the finite LR plate is sharply increased in the band-gap frequency ranges. Furthermore, the acoustic power radiated from the finite LR plate can be seriously affected by its boundary conditions. For the LR plate with greater constraints, the acoustic power is reduced in the band-gap frequency ranges, while that from the one with fully free boundary conditions is increased. When further considering the damping loss factors of the resonators, the attenuation performance can be improved for both the vibration and radiation of the LR plate.

Determining the depth of surface charging layer of single Prussian blue nanoparticles with pseudocapacitive behaviors

2021 ◽  
Author(s):  
wei Wang ◽  
Ben Niu ◽  
Wenxuan Jiang ◽  
Mengqi Lv ◽  
Sa Wang
Keyword(s):  
Prussian Blue ◽  
Electrochemical Impedance ◽  
Modulation Frequency ◽  
Low Frequency ◽  
Frequency Range ◽  
Force Microscopy ◽  
Surface Charging ◽  
Prussian Blue Nanoparticles ◽  
Unit Cells ◽  
Pseudocapacitive Behavior

Abstract Based on the dependence of the light scattering intensity of single Prussian blue nanoparticles (PBNPs) on their oxidation state during sinusoidal potential modulation at varying frequencies, we present an electro-optical microscopic imaging approach to optically acquire the Faradaic electrochemical impedance spectroscopy (oEIS) of single PBNPs. Frequency analysis revealed typical pseudocapacitive behavior with hybrid charge-storage mechanisms depending on the modulation frequency. In the low-frequency range (0.04–1 Hz), the optical amplitude was inversely proportional to the square root of the modulation frequency (i.e., ∆I ∝ f− 0.5; diffusion-limited process), while in the high-frequency range (1.25–100 Hz), it was inversely proportional to the modulation frequency (∆I ∝ f− 1; surface charging process). The contribution of each process was, therefore, determined and quantified using oEIS at the single-nanoparticle level. Because the geometry of single cuboid-shaped PBNPs can be precisely determined by scanning electron microscopy and atomic force microscopy, oEIS of single PBNPs allowed the determination of the depth of the surface charging layer, revealing it to be ~ 2 unit cells regardless of the nanoparticle size.

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