Nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load

This paper focuses on the geometrically nonlinear dynamic analysis of an eccentrically prestressed simply supported damped beam subjected to a concentrated moving harmonic load. The nonlinear dynamic deflections of the beam are obtained by polynomial functions. The Kelvin–Voigt model for the material of the beam is used. Two coupled nonlinear systems of equations of motion are derived using Lagrangeʹs equations under the assumptions of the Euler–Bernoulli beam theory with the von-Kármánʹs nonlinear strain–displacement relationships. The rotary inertia, axial displacement and axial inertia are included in the formulation. The nonlinear equations of motion are solved by using the implicit time integration method of Newmark-β in conjunction with the Newton–Raphson iteration method. In this study, the effects of large deflections, the internal damping of the beam, the velocity of the moving harmonic load, the prestress load, the eccentricity of the prestress load and the excitation frequency on the dynamic response of the beam are discussed. The obtained results are compared with the results based on the linear beam theory. Convergence studies are performed. Numerical results show that the above-mentioned effects play a very important role in the deflections of the beam.