Dynamic displacement response of beam-type structures to moving line loads

A closed-form displacement response of beam-type structures to moving line loads is proposed in this paper. Green's function of the beam on an elastic foundation is obtained by means of Fourier transform. The theory of linear partial differential equation is used to represent the displacement of the beam in terms of convolution of the Green's function. To evaluate this convolution analytically, the theory of complex function is employed to seek the poles of the integrand of the generalized integral. All the poles are identified and given in a closed form. Theorem of residue is then utilized to represent the generalized integral using contour integral in the complex plane. Closed-form displacement is provided and numerical computation is performed. The numerical results show that maximum displacement of a beam with material damping occurs behind the moving load. Also, the maximal dynamic displacement reaches its maximum as the load moves at the critical speed. (C) 2001 Elsevier Science Ltd. All rights reserved.