Wave propagation in two dimensional structures: An efficient solution method in time domain using exponential basis functions

Abstract

In this paper, an efficient time domain formulation is proposed for computing time history dynamic responses of 2D structures, i.e. various types of trusses and frames. Unlike the methods using frequency domain, the proposed method employs the time weighted residual approach to solve the governing differential equations of the axial and flexural wave propagation problems, directly in time. Upon choosing the time step, the solution procedure begins with expressing the variation of axial and transverse displacement components, through the member’s length, as the summations of Fourier exponential basis functions in each time step. The unknown coefficients of the next steps are computed by the implementation of recurrent relations obtained based on a pre-integration process. The equilibrium and necessary continuity conditions at the common nodes/joints of adjacent elements are also fulfilled by introducing an innovative concept utilizing source functions. The role of these source functions is to simulate the boundary effects of the axial and flexural waves propagating within the structural members, simultaneously. The efficiency of the method is demonstrated in the dynamic analysis of some samples of truss and framed structures in terms of accuracy and computational time.