A novel formulation of a spectral plate element for wave propagation in isotropic structures

Authors:
A. Żak
Affiliations:
Institute of Fluid Flow Machinery, Polish Academy of Sciences, Gdansk, Poland
Venue:
Finite Elements in Analysis and Design
Year:
2009

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Abstract

This paper presents a novel formulation of a spectral plate finite element for analysis of propagation of elastic waves in isotropic plate structures. In this formulation of the spectral plate finite element as approximation functions Chebyshev polynomials of the first kind are employed. The element makes use of on an extended form of the displacement field that enables one to investigate selectively or simultaneously both symmetric and anti-symmetric modes of Lamb waves propagating in plate structures. Also the dispersion relations associated with the extended displacement field are presented and discussed in the paper. The effectiveness of the new spectral plate finite element is illustrated on examples of propagation of elastic waves in a flat aluminium panel in the case of the fundamental symmetric and anti-symmetric modes of Lamb waves.