GFEM for modal analysis of 2D wave equation

Abstract

Purpose

The purpose of this paper is to present an application of the Generalized Finite Element Method (GFEM) for modal analysis of 2D wave equation.

Design/methodology/approach

The GFEM can be viewed as an extension of the standard Finite Element Method (FEM) that allows non-polynomial enrichment of the approximation space. In this paper the authors enrich the approximation space with sine e cosine functions, since these functions frequently appear in the analytical solution of the problem under study. The results are compared with the ones obtained with the polynomial FEM using higher order elements.

Findings

The results indicate that the proposed approach is able to obtain more accurate results for higher vibration modes than standard polynomial FEM.

Originality/value

The examples studied in this paper indicate a strong potential of the GFEM for the approximation of higher vibration modes of structures, analysis of structures subject to high frequency excitations and other problems that concern high frequency oscillatory phenomena.

Citation

Torii, A.J., Machado, R.D. and Arndt, M. (2015), "GFEM for modal analysis of 2D wave equation", Engineering Computations, Vol. 32 No. 6, pp. 1779-1801. https://doi.org/10.1108/EC-07-2014-0144