Effect of boundary conditions on the band-gap properties of flexural waves in a periodic compound plate

2017 ◽  
Vol 395 ◽  
pp. 102-126 ◽  
Author(s):  
Zhiwei Guo ◽  
Meiping Sheng ◽  
Jie Pan
Keyword(s):  
Boundary Conditions ◽  
Band Gap ◽  
Flexural Waves ◽  
Compound Plate

scholarly journals Creating the Coupled Band Gaps in Piezoelectric Composite Plates by Interconnected Electric Impedance

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1656 ◽  
Author(s):  
Lin Li ◽  
Zhou Jiang ◽  
Yu Fan ◽  
Jun Li
Keyword(s):  
Band Gap ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Forced Response ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
Flexural Wave ◽  
Response Analysis ◽  
Flexural Waves ◽  
Single Wave

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electric and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electric wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). The features of the coupled band gap are validated by a forced response analysis. We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to adaptively create band gaps.

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.

A Hybrid Solution for Band-Gap Analysis of Vertical Vibration for Periodic Beam-Plate Coupled Systems Based on Variation Principle

2021 ◽  
pp. 2150173
Author(s):  
Qingsong Feng ◽  
Chengxin Dai ◽  
Wenjie Guo ◽  
Zhou Yang ◽  
Jianfei Lu
Keyword(s):  
Boundary Conditions ◽  
Band Gap ◽  
Composite Structures ◽  
Gap Analysis ◽  
Periodic Structures ◽  
Ritz Method ◽  
Coupled Systems ◽  
Variation Principle ◽  
Arbitrary Boundary ◽  
Hybrid Solution

The variation principle widely used in structural dynamics analysis allows us to transform the differential equation of the boundary value problem into a functional with extreme value. In recent years, it has been applied to the band-gap analysis of periodic structures. However, for periodic beam-plate composite structures with periodic and ordinary boundaries, it is relatively difficult for the traditional energy methods, such as the Rayleigh–Ritz method, to construct the displacement functions that satisfy boundary conditions. Hence, a hybrid solution is proposed in this paper to account for various boundary conditions of the periodic beam-plate composite structure. Specifically, the displacement functions constructed by the plane wave series can automatically satisfy the periodic boundary conditions. With the ordinary boundaries modeled by artificial springs, the spectral functions conforming to arbitrary boundary conditions are used to represent the displacement functions. The proposed solution is used to solve the band-gap problems of CRTS-III and CRTS-II slab ballastless tracks in China, and the accuracy of the solution is verified by comparing the calculated results with numerical simulations. In addition, through band-gap formation mechanism analysis, the frequency range of propagating flexural waves in each track component is accurately evaluated, which provides a theoretical basis for refined structural vibration reduction in the future. The solution proposed in this paper is flexible and convenient, which can be extended to a more complex band-gap analysis of periodic structures.

Wave Propagation in Periodically Supported Nanoribbons: A Nonlocal Elasticity Approach

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Giuliano Allegri ◽  
Fabrizio Scarpa ◽  
Rajib Chowdhury ◽  
Sondipon Adhikari
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Nonlocal Elasticity ◽  
Graphene Nanoribbons ◽  
Stop Band ◽  
Flexural Waves ◽  
Finite Element Approach ◽  
Analytical Formulation ◽  
Simply Supported ◽  
Element Approach

We develop an analytical formulation describing propagating flexural waves in periodically simply supported nanoribbons by means of Eringen's nonlocal elasticity. The nonlocal length scale is identified via atomistic finite element (FE) models of graphene nanoribbons with Floquet's boundary conditions. The analytical model is calibrated through the atomistic finite element approach. This is done by matching the nondimensional frequencies predicted by the analytical nonlocal model and those obtained by the atomistic FE simulations. We show that a nanoribbon with periodically supported boundary conditions does exhibit artificial pass-stop band characteristics. Moreover, the nonlocal elasticity solution proposed in this paper captures the dispersive behavior of nanoribbons when an increasing number of flexural modes are considered.

Coupled Band Gaps in the Piezoelectric Composite Plate With Interconnected Electric Impedance

2018 ◽  
Author(s):  
Lin Li ◽  
Zhou Jiang ◽  
Yu Fan ◽  
Jun Li
Keyword(s):  
Band Gap ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Single Wave ◽  
Electric Parameters ◽  
Sub Wavelength

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electrical and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electrical wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to create sub-wavelength band gaps.

Development of curved beam periodic structure in broadband resonance suppression for cylindrical shell structure

2015 ◽  
Vol 23 (8) ◽  
pp. 1267-1284 ◽  
Author(s):  
Xiuchang Huang ◽  
Jinpeng Su ◽  
Longlong Ren ◽  
Hongxing Hua
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Band Gap ◽  
Dynamic Model ◽  
Periodic Structure ◽  
Shell Structure ◽  
Curved Beam ◽  
Isolation System ◽  
Vibration Transmission

A dynamic model is developed to incorporate a curved beam periodic structure in the transfer path of an internal isolation system to reduce the resultant vibro-acoustic of the receiving cylindrical shell structure in a passive broadband way. The vibration transmission from the multi-connected internal isolation system with/without the curved beam periodic structure is built by the matrix method. The analytical representation of the curved beam is employed to establish the transfer matrix dynamic model of the proposed multi-layer curved beam periodic structure. Both numerical simulations and experimental investigations are carried out. The numerical simulations demonstrate that the resonances of the internal isolation system will magnify the vibro-acoustic responses notably and the designed curved beam periodic structure is an effective band-stop mechanical filter to minimize the vibration transmission and acoustic radiation responses at resonances in the band gap. The experimental results confirm that the normal acceleration responses on both the bases and the surface of the cylindrical shell are reduced in the band gap of the curved beam periodic structure. An average reduction amount of 9∼12 dB on the bases and 2∼3 dB on the shell is obtained. The vibration transmission in the curved beam periodic structure is tested and found to be influenced by the boundary conditions at the input and output ends, which is different from that under the free boundary conditions.

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