Spectral element based solutions for wave propagation analysis of multiply connected unsymmetric laminated composite beams

Abstract

A spectrally formulated element that has three degrees of freedom (axial motion, transverse motion and rotation) per node for analysis of slender multiply connected composite beams under high-frequency impact loading is presented. The model represents a linear distributed parameter system. The element has an exact dynamic stiffness matrix as it is derived from exact solution to the governing wave equation in frequency domain. The present element can handle any kind of cross-sectional unsymmetry due to ply orientation. The results from the present formulation are compared with the results from a time domain finite element model based on linear axial and cubic transverse displacement field. It is shown that the formulated element is able to predict the reflected and transmitted response accurately through a rigid angle joint for varying joint angles and axial–flexural coupling. Also, the effect of ply-stacking sequence on dynamic response is illustrated. With this approach, a very large composite 2-D beam network can be analyzed under high-frequency impact loading with much smaller system size and lower computational cost compared to time domain finite element method.