Nonlinear oscillations and transmissibility of a beam subject to a reciprocating moving load and mounted on viscoelastic supports

This paper presents a new nonlinear dynamic model and analysis of a viscoelastic beam mounted on viscoelastic supports and excited by a reciprocating moving load. The equation of motion is derived by the extended Hamilton’s principle and solved utilizing the harmonic balance method. The nonlinear frequency response and force transmissibility characteristics for various loads and boundary conditions are demonstrated. Parametric analysis is performed to explore the influence of several nondimensional quantities on the frequency response and transmissibility. The effect of rigid–flexural motion interactions on the nonlinear dynamic behavior of the system is investigated. Moreover, the effects of the supports’ stiffness symmetry and magnitudes on the nonlinear response and force transmissibility characteristics are thoroughly examined. The influence of internal damping is found to be minimal for low support stiffness, whereas a significant effect is observed for high support stiffness.