DYNAMIC RESPONSE TO A MOVING LOAD OF A HIGHLY PRESTRESSED ISOTROPIC RECTANGULAR PLATE ON A BI-PARAMETRIC SUBGRADE

Abstract

In this thesis, the dynamic response of a highly prestressed isotropic rectangular plate resting on a bi-parametric subgrade under the action of a moving load is investigated. In particular, the bi-parametric subgrade is the so called Pasternak foundation model. The equation of motion of the dynamical system which is a fourth order non-homogeneous partial differential equation is presented in a non-dimensionalized form. As a result of this, a small parameter E (the ratio-of bending stiffness to the axial prestress) multiplies the highest derivative in the governing partial differential equation. For an analytical solution to be obtained, the equation was subjected to Laplace transformation while the resulting partial differential equation was solved using the singular perturbation technique, specifically the Method of Matched Asymptotic Expansion (MMAE). The methods of integral transformations and the Cauchy residue theory were then used to solve the resulting partial differential equations to obtain a uniformly valid analytical solution in the entire domain of definition of the rectangular plate. Analysis of analytical solutions and numerical results in plotted curves were presented. The results show that the prestress, shear modulus and foundation stiffness affect the response to 0(£1) of the rectangular plate. Also, the critical velocities of the dynamical system increase with prestress, shear modulus and foundation stiffness. Thus, resonance is reached earlier for lower values of prestress, shear modulus and foundation stiffness.