Vibration of Prestressed Isotropic Rectangular Plate with General Boundary Conditions and Under Partially Distributed Loads Moving at Varying Velocities

Abstract

The dynamic analysis of prestressed rectangular plate with general boundary conditions and under partially distributed loads moving at varying velocities is investigated in this paper. A procedure involving the generalized two-dimensional integral transform with beam functions as kernel of transformation is used to reduce the governing fourth order partial differential equation to a second order coupled ordinary differential equation. The Struble’s asymptotic technique is then   used to simplify this equation to make it amenable to the methods of integral transformation and convolution theory. By means of these, the analytical solution valid for all variants of classical boundary conditions to the dynamical problem is obtained. The analytical solution and numerical analysis show that the critical speed for the moving distributed mass problem is reached earlier than that of the moving distributed force problem for both illustrative examples considered. The results further show that an upward variations of foundation stiffness K, rotatory inertia correction factor R0, subgrade modulus G and axial force N decrease the response amplitude of the rectangular plate. Finally, for fixed pertinent structural parameters, the transverse displacement response of the rectangular plate under moving partially distributed forces is not an upper bound to the case when subjected to moving partially distributed masses. Hence, safety is not guaranteed for a design based on the moving partially distributed force problem.