Dynamic response of an infinite timoshenko beam periodically supported subjected to a moving load

Abstract

This study proposes an analytical approach to calculate the wave pattern produced by a moving load on a periodically supported Timoshenko beam. The Green's function for an unsupported beam is first assessed. Supports are then integrated using superposition, expressing the overall response as a combination of reactions from all supports and the external force. Bloch's theorem accounts for support periodicity, leading to a uniform system governed by a differential equation describing the rail response. Solving the homogeneous case derives the dispersion equation for Bloch waves and wave bands. The Bloch waves and dispersion curves represent the underlying mechanics of this dynamic scenario. The dynamic load creates a wave field expressed as a Bloch wave superposition, similar to modal decomposition for finite structures. The methodology determines the wave pattern from a constant velocity load traveling along a slender, periodically supported Timoshenko beam.