AXIAL FORCE INFLUENCE ON THE RESPONSE TO MOVING CONCENTRATED MASSES OF RECTANGULAR PLATES INCORPORATING ROTATORY INERTIA CORRECTION FACTOR.

Abstract

This thesis studies the influence of axial force on the dynamic response to moving concentrated masses of rectangular plate incorporating rotatory inertia correction factor. The responses of the elastic structures to moving concentrated forces are special cases of such dynamical problems. The governing equation 0 f this problem is a fourth order partial differential equation. The solution technique is based on the use of the property of the Diracdelta function as an even function to express it in series form. the versatile two dimensional generalized integral transform with the normal modes of the plate as the kernel of transformation and a modification of the Struble's asymptotic technique. By the use of this technique, one is able to obtain closed form solutions for all variants of classical end conditions for this class of problems. The closed form solutions are analysed and numerical analyses in plotted curves are presented. The results show that as the axial force (prestress), Nx and Ny, foundation moduli K and rotatory inertia Ro increase, the response amplitudes of the dynamical system decrease for both illustrative examples. However, higher values of N; Ny, K and Ro are required for a more noticeable effect in the case of simple clamped boundary conditions than those. of simply supported boundary conditions. It is also found that for both illustrative examples, the moving force solution is 110t an upper bound for the accurate solution of the moving mass problem of a VII rectangular plate under the action or a concentrated moving load. This important result also agrees with the result of similar problems in literature. Finally, in all the illustrative examples considered, 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 moving mass problem.