On the Response to Distributed Loads of Elastic Isotropic Rectangular Plate Moving with Varying Velocities

Abstract

The dynamic behaviour of a simply supported rectangular plate moving with non-uniform velocities is investigated in this paper. The inertia and gravity effects of the moving load are taken into consideration. In order to solve the governing fourth order partial differential equation, a technique based on two-dimensional finite Fourier sine integral transformations, modification of Struble’s asymptotic technique and Fresnel sine and Fresnel cosine identities were used. The closed form solutions are obtained and numerical analyses in plotted curves are presented. The results show that as the foundation stiffness K and other structural parameters increases, the response amplitude of the simply supported rectangular plate resting on Pasternak foundation decreases. It is also shown that for fixed  value of foundation stiffness K, axial force N, shear modulus G and rotatory inertia correction factor R0, the transverse deflections of the rectangular plate under the action of moving distributed masses are higher than those when only force effects of the moving load is considered. This implies that resonance is reached earlier in moving partially distributed mass problem than in moving distributed force problem.