Torsional vibration of thin-walled elastic beams with doubly-symmetric cross-sections traversed by concentrated masses

Abstract

In this paper, the problem of analyzing the torsional vibration of thin-walled elastic beams, with open cross-sections that are doubly symmetric and traversed by moving concentrated masses at constant speeds is addressed. The mathematical model adopted accounts for both the gravitational and inertial effects of the moving loads, thus making the problem a moving-force moving-mass problem. Variable coefficients with strong singularities are therefore present in the characterizing differential equation. By means of Green’s function of the associated moving-force problem, the complete moving-force moving–mass problem is transformed into an integrodifferential equation. An iteration scheme for solving the integro-differential equation has been proposed and shown to converge to a unique continuous function of space and time, the only solution to the equation.

Journal of the Nigerian Association of Mathematical Physics, Volume 15 (November, 2009), pp 55 - 70