Dynamic coefficient of flexural motion of beam experiencing simple support under successive moving loads

Abstract

Analytic expressions of the dynamic coefficient (DC) factor and vibrational behavior of a uniformly elastic isotropic beam with a simple boundary condition caused by accelerating masses with varying velocities are analyzed. The motion of this problem is described by a fourth-order partial differential equation, which governs its behavior. The weighted residual method converts the governing equation into a sequence of linked second-order differential equations to facilitate the analysis. A rewritten version of Struble's asymptotic method further simplifies the transformed governing equation. This modification aids reduction in the complexity of the equation. The closed-form response is contrasted across three force motions: acceleration, deceleration, and uniform motion. The study thoroughly examines how different velocities and frequencies of the moving force affect the dynamic behavior of the beam. The study also examines the influence of load velocity on the DC of the beam subjected to pinned–pinned boundary conditions.