Study on the Dynamic Response of Single and Multi-Spans Beam Subjected to the Base Excitation Using Time Weighted Residual Method

Accurate determination of the response of structures under dynamic loads such as earthquake loads plays an important role in the safe and economical design of structures. The purpose of this paper is to utilize a novel solution method based on the use of exponential basis functions for dynamic analysis of Bernoulli beam subjected to different types of base excitations. This method was firstly introduced for solving scalar wave propagation problems, named as stepwise time-weighted residual method. The proposed method considers the solution as a series of exponential basis functions with unknown constant coefficients; and the problem is solved in time without the need for spatial discretization of the beam and by using an appropriate recursive relation to correct the coefficients of the exponential bases. In order to apply the earthquake excitation, first by using the central finite difference relation, the earthquake acceleration history is converted to displacement history. Moreover, the displacement history is applied to the beam as a time-varying boundary condition. In this study, the capabilities of the proposed method in solving several sample problems of vibration of single and multi-span beams under various stimuli such as earthquake acceleration variations are compared with the results of other existing methods.