Analyzing first symmetric and antisymmetric Lamb wave modes in functionally graded thick plates by using spectral plate elements.

Highlights • The new series of differential equations of free vibration of thick functionally graded plates, including the lateral extension, have been derived. • Based on the dispersion relation and Lamb wave velocity, the validation of the differential equations has been investigated. • Legendre spectral element method is utilized to analyze the thick functionally graded plates subjected to impulsive loading. • The accuracy of the numerical simulation is examined by comparing the group wave velocity of first symmetrical and asymmetrical modes of Lamb waves derived from the dispersion relations and numerical models. Abstract In this paper, a new series of differential equations which can predict the propagation and dispersive behavior of first symmetric and antisymmetric Lamb wave modes in functionally graded material (FGM) thick plates are developed. Then, given the accuracy and cost effectiveness of Legendre spectral element method in combination with central difference method, these methods are utilized to set up the numerical models and solving the dynamic discretized differential equations. Finally, based on the wave front velocity, the percentage of error is estimated and it is shown that considering some limitations which are inherently included in the utilized method of error estimation, the proposed equations and the numerical procedure can predict the behavior of first symmetric and antisymmetric Lamb wave modes in FGM thick plates precisely. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]