Nonlinear Vibration Analysis of a Hinged–Clamped Beam Moving with Pulsating Speed and Subjected to Internal Resonance

Abstract

This work focuses on the revelation of nonlinear characteristics of a hinged–clamped beam moving with pulsating speed. Cubic geometric nonlinearity, viscous damping due to intervening medium, and viscoelastic material damping are considered in the governing equation of motion. Parametric excitation is induced in the system due to pulsating speed amid 3:1 internal resonance between the first two modes. A perturbation technique-direct method of multiple scales is applied to solve the problem. Nonlinear features like various stability and bifurcation phenomena are extracted by applying a continuation algorithm. Trivial state stability plot and the impacts of viscous and material damping have been studied. The consequence of alterations of the amplitude of pulsating speed constituent, internal frequency detuning parameter, axial stiffness, and parametric detuning parameter on the vibration responses have been analyzed in detail. The analytic-numeric approach reveals rich and interesting nonlinear phenomena under united parametric and internal resonances in the study of the hinged–clamped beam that are not available in the existing literature.