Elasto-dynamic analysis of a general orthotropic finite layer resting on flexible foundation under moving loads

Abstract

The vibration of a general orthotropic finite layer resting on the flexible foundation under transverse and shear point loads moving with a constant velocity on the layer boundary is studied. Structural energy dissipation in the layer and foundation and the foundation flexibility are modeled by viscous dampers and linearly distributed transverse and axial springs, respectively. Equations of motion for the analyses of slender and thick orthotropic layers resting on the flexible foundation are derived. The solution to these equations for orthotropic layers, with any elasticity boundary conditions at the ends, is accomplished by employing the integral transform and generalized differential quadrature methods. The effects of structural energy dissipation, the orientation of material principal axes of orthotropy, and load velocity on the stress and deflection fields of the layer are studied. Contrary to the conventional beam models, the elasticity solution considers the normal stress component in the thickness direction, resulting in a more accurate solution. In various beam theories equations defining displacement components in thickness direction should be assumed a priori, whereas using the elasticity theory the beam displacement field is a part of the solution. Moreover, the elasticity theory is capable of accurately analyzing thick beams.