Vibration Analysis of Thin Plate Structures Subjected to a Moving Force Using Frequency-Domain Spectral Element Method

Abstract

A frequency-domain spectral element method (SEM) is proposed for the vibration analysis of thin plate structures subjected to a moving point force. The thin plate structures may consist of multiple rectangular thin plates with arbitrary boundary conditions that form multispan thin plate structures, such as bridges. The time-domain point force moving on a thin rectangular plate with arbitrary trajectory is transformed into a series of stationary point forces in the frequency domain. The vibration responses induced by the moving point force are then obtained by superposing all vibration responses excited by each stationary point force. For the vibration response of a specific stationary point force, the plate subjected to the specific stationary point force is represented by four spectral finite plate elements, which were developed in the authors’ previous work. The SEM-based vibration analysis technique is first presented for single-span thin plate structures and then extended to the multispan thin plate structures. The high accuracy and computational efficiency of the proposed SEM-based vibration analysis technique are verified by comparison with other well-known solution methods, such as the exact theory, integral transform method, finite element method, and the commercial finite element analysis package ANSYS.