Analytical solution for a finite Euler–Bernoulli beam with single discontinuity in section under arbitrary dynamic loads

Abstract

• Analytical solution is derived for finite beam on viscoelastic foundation to arbitrary loads. • The foundation has a step change at the discontinuous section of the beam. • The modal shape superposition scheme is used to obtain explicit solution. • The distinct beam element method is employed for free vibration analysis. • Degraded solutions for two special loads are expressed and validated. In this paper, the dynamic response of a finite Euler–Bernoulli beam with single discontinuity in section lying on viscoelastic foundation subjected to arbitrary dynamic loads is investigated. The viscoelastic foundation has a step change at the discontinuous section of the beam. Based on the modal superposition method, the explicit formulations of the problem are obtained for beam deflection, velocity, acceleration, bending moment and shear force. The natural frequencies and corresponding modal shape functions of the beam are obtained by imposing continuity at the contact between different components of the beam. The solution is verified by providing comparisons between its results and those from the Finite Element program ABAQUS.