Moving-Inertial-Loads-Induced Dynamic Instability for Slender Beams Considering Parametric Resonances

This paper investigates the moving-inertial-loads-induced dynamic instability limit for transverse bending vibration of slender beams considering both simple and combination parametric resonances under disturbances on multiple modal coordinates. The vibration system is described in the modal domain using ordinary differential equations with periodic parameters. Straightforward expansion is conducted to analyze the possible resonance regions. The impulsive parametric excitation method is employed to compute the monodromy matrices. System dynamic stability is evaluated and the transition curves are computed. Numerical studies on single-span clamped–clamped and clamped–hinged beams considering the first two modes are conducted. The computed dynamic instability maps verify the analytically derived resonance occurrence conditions and present the following observations. The initial disturbances on multiple modes will induce variation of the parametric resonance instability region and create new resonance tongues. Among all resonance tongues, principal simple and sum combination resonance tongues are the most important. For the mitigation of combination resonances, damping measures are required to be applied on all related modes.