Dynamic Influence of Foundation Stiffness on Rectangular Structural Plate with Constant Bi-parametric Elastic Foundation with Simple Elastic End Conditions.

Abstract:

This paper considers the dynamic influence of foundation stiffness such as foundation modulus, shear modulus, Young modulus as well as rotatory inertia correction factor on the vibrations of orthotropic rectangular structural plate resting on a constant bi-parametric elastic foundation with simple elastic end conditions when moving distributed loads are traversing on the structural plate. The orthotropic rectangular structural plate model is a coupled fourth order partial differential equation with variables and singular coefficients. The solutions to the model are obtained by transforming the fourth order partial differential. The fourth order partial differential equation is transformed to a set of coupled second order ordinary differential equations by using a special technique adopted by Shadnam et al [11]. This set of second order ordinary differential equations is then simplified using modified asymptotic method of Struble. The closed form solution is analyzed, resonance conditions are obtained and the results are presented in plotted curves to show the impact of foundation parameters for both cases of moving distributed mass and moving distributed force.