Wave-based in-plane vibration analysis of multiple coupled beam structures with arbitrary connection angle and elastic boundary restraints

Beam structures are widely used in various engineering branches, and the investigation on their dynamic behavior is of fundamental significance for the efficient design and vibration control of complex beam structures. In this work, a unified wave-based model for the in-plane vibration analysis of multiple coupled beams with arbitrary connection angle and boundary conditions is established, in which the vibrations within structures are described as wave propagation along structural elements, accompanying with wave reflection and transmission at some particular positions (such as the boundaries or structural joints). The reflection and transmission matrices corresponding to the incident waves propagating to the angular joint from various directions and the wave reflection matrix at the elastic boundary are derived. The natural and forced in-plane vibrations of multiple coupled beams can be analyzed concisely and systematically by assembling these wave reflection and transmission matrices. The accuracy of this approach is validated by comparing the dynamic characteristics obtained by the current approach with finite element method. Then, the influences of boundary stiffnesses and joint angle on wave reflection and transmission matrices are investigated. The results show that it is possible to know which wave type is dominant in structure at a certain frequency or angle, which shows certain significance for future work of vibration control and power flow analysis. The unified analysis model established in this paper can not only analyze the vibration characteristics of complex coupled beams but also reveal how waves are reflected and transmitted in the structure.