Vibrations of a Non-Homogenous Timoshenko Beam on a Two-Parameter Foundation Subject to a Moving Load

Transverse vibrations of a simply supported Timoshenko beam resting on a two parameter elastic foundation under moving concentrated load are analysed. The vertical variation of Young's modulus through the beam is considered. The supplementary modulus of elasticity and shear coefficient of beam are included into equations of motion. The beam rests on the foundation characterized by two moduli: the Winkler foundation modulus and the shear foundation modulus (Pasternak model). The response of the Timoshenko beam is found from the governing equations of motion. Forced and free vibrations of the beam are analysed. The solutions are illustrated by some numerical examples.