%0 Journal Article
%T Dynamic Analysis of a Timoshenko Beam Subjected to an Accelerating Mass Using Spectral Element Method
%A Guangsong Chen
%A Linfang Qian
%A Qiang Yin
%J Shock and Vibration
%D 2014
%R 10.1155/2014/768209
%X This paper presents formulations for a Timoshenko beam subjected to an accelerating mass using spectral element method in time domain (TSEM). Vertical displacement and bending rotation of the beam were interpolated by Lagrange polynomials supported on the Gauss-Lobatto-Legendre (GLL) points. By using GLL integration rule, the mass matrix was diagonal and the dynamic responses can be obtained efficiently and accurately. The results were compared with those obtained in the literature to verify the correctness. The variation of the vibration frequencies of the Timoshenko and moving mass system was researched. The effects of inertial force, centrifugal force, Coriolis force, and tangential force on a Timoshenko beam subjected to an accelerating mass were investigated. 1. Introduction Dynamic response of structures subjected to a moving force or moving mass is an important issue in engineering problems. For example, the trains have experienced great advances characterized by increasingly higher speeds and weights of vehicles. As a result, the dynamic response, as well as stresses, can be significantly higher than that before or static loads. The problem arose from the observations is a structure subjected to moving masses. Many researchers studied these problems and many studies are presented in the literatures. For examples, references [1¨C3] assuming the moving load to be a moving force have given some analytical solutions. Abu-Hilal [4] studied the dynamic response of a double Euler-Bernoulli beam due to a moving constant load. Fryba [5] extensively analyzed the solution of moving loads on structures. Rao [6] gave a detailed analysis of the vibration of a beam excited by a moving oscillator using a perturbation method. Zibdeh and Juma [7] presented the dynamic response of a rotating beam subjected to a random moving load using analytical and numerical methods. Akin and Mofid [8] investigated the dynamic behavior of Bernoulli-Euler beams carrying a moving mass with different boundary conditions using analytical-numerical method, and achievements by other researchers are presented in literatures [9¨C14]. The studies mentioned are based on Bernoulli-Euler beam, while the moment of inertia and shear deformation should be taken into account when ratio of the height to span is large. References [15¨C20] studied the dynamic response of Timoshenko beams subject to moving force. Ross [21] studied the problem of a viscoelastic Timoshenko beam subjected to a step-loading using the Laplace transform method. Katz et al. [22] solved the dynamic response of a rotating
%U http://www.hindawi.com/journals/sv/2014/768209/