Forced Flexural Vibrations of an Elastic Beam Supported by an Elastic Half-Space

Abstract

This paper investigates analytically the plane stress problem of flexural vibrations of an elastic beam supported by an elastic half-space and subjected to a sinusoidally varying force at the free end of the beam. Since the actual stress and displacement distributions at the interface between the half-space and beam are still unknown, we assume linear normal stress distribution and uniform shear stress distribution at the interface, and apply mean displacement and mean slope of the half-space. The dynamic effects of foundation stiffness and slenderness ratio on the response curves of the beam are presented.