Abstract
The flexural motions of elastically supported rectangular plates carrying moving masses and resting on variable Winkler elastic foundations is investigated in this work In order to solve the fourth order partial differential equation governing the problem, a technique based on separation of variables is used to reduce the governing fourth order partial differential equations with variable and singular coefficients to a sequence of second order ordinary differential equations. These equations are then solved using a modification of the Struble's technique and method of integral transformations. Numerical results are then presented in plotted curves. The results show that response amplitudes of the plate decrease as the value of the rotatory inertia correction factor Ro increases and for fixed value of Ro, the displacements of the elastically supported rectangular plates resting on variable elastic foundations decrease as the foundation modulus Fo increases. Also, for fixed Ro and Fo, the transverse deflections of the rectangular plates under the actions of moving masses are higher than those when only the force effects of the moving load are considered. Therefore, the moving force solution is not a safe approximation to the moving mass problem. Hence, safety is not guaranteed for a design based on the moving force solution. Furthermore, the results show that the critical speed for the moving mass problem is reached prior to that of the moving force for the elastically supported rectangular plates on Winkler elastic foundation with stiffness variation.
Highlights
The analyses of elastic structures, such as beams and plates, acted upon by moving loads and resting on a foundation constitute an important part of Engineering and applied Mathematics literatures
The objective of the work has been to study the problem of the dynamic response to moving concentrated masses of rectangular plates on variable Winkler elastic foundations
The closed form solutions of the fourth order partial differential equations with variable and singular coefficients of the rectangular plate is obtained for both cases of moving force and moving mass
Summary
The analyses of elastic structures, such as beams and plates, acted upon by moving loads and resting on a foundation constitute an important part of Engineering and applied Mathematics literatures. Douglas et al (2002) solved the problem of plate strip of varying thickness and the center of shear In their work, they considered a free-vibrating strip with classical boundary conditions, precisely, they assumed the plate strip clamped at one end and free at the other end. In a recent development, Oni and Awodola (2005) investigated the dynamic response to moving concentrated masses of uniform Rayleigh beams resting on variable Winkler elastic foundation. Oni and Awodola (2010) considered the dynamic response under a moving load of an elastically supported non-prismatic Bernoulli-Euler beam on variable elastic foundation. This study concerns the response to moving concentrated masses of elastically supported rectangular plate resting on Winkler elastic foundation with stiffness variation
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