Nonlinear Primary Resonance Behaviors of a Double-Beam System Resting on an Elastic Foundation

The double-beam system made up of two interconnected parallel beams is one of the most significant mechanical models in modern engineering structures. However, few studies have focused on the nonlinear characteristics of double-beam systems. This paper strives to investigate the nonlinear primary resonance behaviors of double-beam systems interconnected by a viscoelastic layer driven by the transverse harmonic excitation, in a systematic manner. By combining the Galerkin method and the incremental harmonic balance method, the iterative formula for periodic responses is determined and then corrected via the two-point pseudo-arclength algorithm to overcome difficulties of numerical continuation around bifurcation points. Numerical examples are performed to verify the present solutions and explore the effects of various parameters on the resonance behaviors of the double-beam system in detail. Outcomes first demonstrate that the multi-valued region of the in-phase resonant peak of the system can achieve partial or even full coverage that of the out-of-phase resonant peak, which indicates that applying disturbances in the intersection region may realize mutual conversion between the in-phase and out-of-phase vibration patterns, and this intriguing behavior does not occur in a single-beam system, in general. It is highlighted that, by adjusting system parameters, such as increasing the connecting layer stiffness or decreasing the excitation amplitude, the out-of-phase resonant peak can be detached from the coverage region of the in-phase one. The present findings may serve as a new starting point for engineering applications of double-beam systems.