On Modal-Asymptotic Analysis to Prestressed Thick Beam on Bi-Parametric Foundation Subjected to Moving Loads

Abstract

In this paper, the dynamic response of prestressed thick beam subjected to moving loads using modal-asymptotic analysis (MAA) is investigated. The main objective of this work is to obtain an analytical closed-form solution to this class of dynamical problems. To use MAA, accurate information is needed on the natural frequencies, mode shapes, orthogonality of the mode shapes, and Stubble’s Asymptotic technique a prior. A thorough literature survey reveals that the method has not been reported in the existing literature, even for simple Timoshenko beams. Thus, we present complete information on how to use the MAA to derive the forced vibration responses of a simply supported Timoshenko beam subjected to moving loads. The effects of prestress, foundation parameters, and moving velocity on the dynamic characteristics of the beams are studied and described in detail. To validate the accuracy of this method, we compare the frequency parameter with the existing literature which is shown to compare favorably.