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 multi-source excitation. A dynamic model is established using energy variational and Hamilton’s principles. Numerical solutions are obtained via an improved Galerkin-based 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 phase-sensitive bands and trigger boundaries. Peak displacements are strongly nonmonotonic 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.