ROTATORY INERTIA INFLUENCE ON THE DYNAMIC RESPONSE TO MOVING MASSES OF RECTANGULAR PLATES ON A NON-WINKLER ELASTIC FOUNDATION

Abstract

This thesis is concerned, in general, with the study of the influence of rotatory inertia on the dynamic response to moving concentrated masses of rectangular plates on a non- Winkler elastic foundation. Specifically, the equation of motion is not governed by the classical two-dimensional theory of flexural motions of thin plate where the effect of rotatory inertia is neglected. In addition, the plate rests on a non-Winkler elastic foundation, in particular, the Pasternak Subgrade. In order to solve this problem, the property of the Dirac-delta function as an even function is used to express it in series form and the versatile two dimensional generalized integral transforms is used to reduce the fourth order partial differential equation with singular coefficients to a coupled second order ordinary differential equation. For the solution of this equation, a modification of the Struble's asymptotic technique is' employed. The analytical solutions are analyzed and numerical results in plotted curves are then presented. The results show that as the rotatory inertia correction factor increases the response amplitudes of a rectangular plate resting on a Pasternak Subgrade and under the actions of moving masses decrease. This result holds for both Simply Supported and Simple-Clamped plate and for both moving force and moving mass problems. Furthermore, it is found that the response amplitudes of a rectangular plate resting on a Pasternak Subgrade decrease with an increase in the values of shear modulus G for fixed values of foundation's stiffness K and rotatory inertia Rot. Similarly, as K increases the response amplitudes decrease but effect of G is more noticeable than that of K. Finally, for both Simply Supported and Simple-Clamped rectanr ulur plate, under moving concentrated masses, for the same natural frequency, the critical speed for the moving mass problem is smaller than that of the moving force problem. Hence resonance is reached earlier in the former.