Analysis of Lateral Dynamic Behavior in Coupled Beams with Nonlinear End Coupling

As a fundamental structural form, beam structures are widely used in fields such as architecture, navigation, and aerospace. When analyzing complex structures in engineering, they are typically divided into several substructures, and the coupling relationships between these substructures are established to simulate real-world conditions. With the development of research, scholars have gradually paid attention to nonlinear factors in engineering and introduced them into the elastically coupled structures. However, the existing literature mainly discussed the potential influence of coupling nonlinearities on the dynamic behavior of elastic coupled systems, where such coupled structures were typically subjected to one excitation. It is of great engineering significance to study the dynamic behavior of elastic structures with nonlinear coupling factors affected by multi-source excitations. This work presents a vibration analysis model of a coupled beam system with a nonlinear coupling term at the end, which is subjected to double excitations. The numerical lateral magnitudes of CB 1 and CB 2 can be precisely calculated using the Galerkin truncation method (GTM). Within a specific range, increasing [Formula: see text] introduces additional resonance magnitudes into the numerical lateral dynamic response curve of CB 1 and CB 2. When [Formula: see text] rises to a certain threshold, multi-solution dynamic behavior emerges in the system’s numerical lateral magnitude curve. Blindly increasing [Formula: see text] leads to an abnormal elevation of numerical response magnitudes at certain primary resonance regions of CB 1 and CB 2, which is detrimental to the vibration control of CB 1 and CB 2. Besides, the numerical lateral magnitudes of CB 1 and CB 2 corresponding to different [Formula: see text] values all fall within a fixed region. Due to differences in the phase angles of the external excitations, the numerical lateral magnitudes of each sub-beam in a coupled beam system fluctuate within the numerical lateral magnitude interval.