Flexural Response of a Cantilever Beam under Masses of Varying Velocities with General Boundary Condition

Abstract

Response characteristics of an isotropic Rayleigh beam with general boundary constraints under the influence of dynamic loads are explored. A fourth-order partial differential equation describes and governs the behaviour of this problem. The weighted residual method converts the governing equation into a series of coupled second-order type of differential equations to facilitate the analysis. A revised version of Struble's asymptotic method is utilized to simplify the transformed governing equation further. This modification aids in reducing the complexity of the motion equation. The Duhamel integration method is then used to find closed-form solutions to the problem, which are then contrasted for three different force motions: forward force, retard force, and uniform. Essential factors such as prestressed force, foundation subgrade, rotatory inertial correction factor, beam length, and the speed of moving loads are all carefully examined, and their impacts are established in this study.