Vol. 14, No. 2, 2019

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Elastic wave propagation in a periodic composite plate structure: band gaps incorporating microstructure, surface energy and foundation effects

Gongye Zhang and Xin-Lin Gao

Vol. 14 (2019), No. 2, 219–236
Abstract

A new model for predicting band gaps for flexural elastic wave propagation in a periodic composite plate structure is developed using a non-classical Kirchhoff plate model that is based on a modified couple stress theory, a surface elasticity theory and a two-parameter Winkler–Pasternak elastic foundation model. The formulation is based on the plane wave expansion method and Bloch’s theorem. The current non-classical model simultaneously incorporates microstructure, surface energy and foundation effects, unlike existing models. When the microstructure and surface energy effects are both suppressed, the new model reduces to the classical elasticity-based model. The band gaps predicted by the newly developed model vary with the microstructure-dependent length scale parameters, the surface elastic constants, the elastic foundation moduli, the unit cell size, and the volume fraction. The numerical results reveal that the first band gap including the foundation effect is always smaller than that without considering the foundation effect, and the first foundation band gap size increases with the increase of the elastic foundation moduli. Also, the first band gap predicted by the new non-classical model is always larger than that predicted by the classical model, but the difference is diminishing as the plate thickness increases. In addition, it is found that the sizes of the first band gap and the first foundation band gap decrease with the increase of the unit cell length at different length scales. Furthermore, it is seen that the volume fraction has a significant effect on the sizes of the first band gap and the first foundation band gap, and band gaps can be tailored by adjusting the volume fraction as well as the constituent properties.

Keywords
band gaps, wave propagation, Kirchhoff plate, couple stress, surface elasticity, elastic foundation, plane wave expansion method, Bloch theorem, size effect
Milestones
Received: 20 October 2018
Accepted: 25 December 2018
Published: 29 May 2019
Authors
Gongye Zhang
Jiangsu Key Laboratory of Engineering Mechanics
School of Civil Engineering
Southeast University
Nanjing, Jiangsu
China
Xin-Lin Gao
Department of Mechanical Engineering
Southern Methodist University
Dallas, TX
United States