Dynamic Analysis under Uniformly Distributed Moving Masses of Rectangular Plate with General Boundary Conditions

Abstract

The problem of the flexural vibrations of a rectangular plate having arbitrary supports at both ends is investigated. The solution technique which is suitable for all variants of classical boundary conditions involves using the generalized two-dimensional integral transform to reduce the fourth order partial differential equation governing the vibration of the plate to a second order ordinary differential equation which is then treated with the modified asymptotic method of Struble. The closed form solutions are obtained and numerical analyses in plotted curves are presented. It is also deduced that for the same natural frequency, the critical speed for the system traversed by uniformly distributed moving forces at constant speed is greater than that of the uniformly distributed moving mass problem for both clamped-clamped and simple-clamped end conditions. Hence resonance is reached earlier in the uniformly distributed moving mass system. Furthermore, for both structural parameters considered, the response amplitude of the moving distributed mass system is higher than that of the moving distributed force system. Thus, it is established that the moving distributed force solution is not an upper bound for an accurate solution of the moving distributed mass problem.