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Plane wave finite element model for the 2-D phononic crystal under force loadings by Jian-Fei Lu; Jie Cheng; Qing-Song Feng is a Engineering article available to read on EtoBox.

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## Finite element method Plane wave expansion The point force The eigenvalue problem A B S T R A C T Direct numerical simulations of the dynamic response of the phononic crystal to point or distributed forces via conventional numerical methods are still formidable currently due to large number of DOFs involved in the simulations. In this study, based on the plane wave expansion (PWE) method, a plane wave finite element (PWFE) model for the 2-D phononic crystal which is infinite in the horizontal direction and finite in the vertical direction and subjected to a point harmonic force is proposed. To this end, the point harmonic force is decomposed into the wavenumber domain (WND) components by the Fourier transform first. The variables of the 2-D phononic crystal under the WND force component are expanded into a series of plane waves along the horizontal direction, and the variables associated with each plane wave are discretized by the FE method in the vertical direction. By using the virtual work principle, FE equations for the plane waves of the phononic crystal are established. With the FE equations for the plane waves, the eigenvalue equation for the displacement of the plane wav

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Author

Jian-Fei Lu; Jie Cheng; Qing-Song Feng

Published

2022

Language

EN

Field

Engineering (Physical Sciences)