Modeling and dynamic behavior study of a cross-coupled beam system under multi-source excitation

This study investigates a transversely inclined coupled beam system under multisource excitation. A dynamic model is established using energy variational and Hamilton’s principles. Numerical solutions are obtained via an improved Galerkinbased Truncation Method (GTM), validated with an independent Lagrange approach. Numerical results indicate that coupling stiffness significantly alters modal distributions and amplitude-frequency responses, leading to frequency shifts and peak rearrangements. The phase difference between identical-frequency excitations acts as a key control variable. Analysis of displacement envelopes and polar plots reveals phasesensitive bands and trigger boundaries. Peak displacements are strongly non-monotonic and asymmetric with phase, exhibiting directional phase-locking at higher frequencies. The study demonstrates that adjusting the excitation phase, without adding mass, can effectively control vibration and resonance. This provides a basis for integrating nonlinear connections or innovative materials to achieve adaptive phase-stiffness control, with practical relevance for beam-type substructures in medical, wind turbine, and aerospace applications.