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.
