Vibration and bandgap characteristics analysis of multiple beams with arbitrary connection angles

Abstract

Multi-coupled beam structures can be encountered in a wide range of engineering disciplines. Due to the possible periodicity of structures, it is important to investigate their vibration and bandgap characteristics. In this study, an accurate wave-based analytical model for the in-plane vibration of a multi-coupled beam structure with arbitrary coupling angles is developed. The reflection and transmission matrices corresponding to the incident waves arriving at the angular junctions from different directions are derived. By combining these reflection and transmission matrices, the free and forced vibrations of the multi-coupled angle beam structures can be analyzed systematically and concisely. The theoretical analysis results are in good agreement with those calculated from the FEM analysis results, which verifies the accuracy of the current method. Moreover, the analytical expression of the bandgap characteristics of infinite multi-coupled beam structures is formulated. The bandgap characteristics results of the infinite multi-coupled beam structures coincide well with the frequency response function (FRF) of the finite multi-coupled beam structures, which verifies the correctness of the analytical expression of bandgap analysis. Further results show that a low-frequency and wide bandgap can be obtained by choosing the appropriate lattice constants and junction angles, which has positive significance for the efficient design and vibration attenuation of multi-coupled beam structures in practical engineering.