Dynamic response and power flow in three-dimensional coupled beam structures. I. Analytical modeling

摘要

This paper deals with the prediction of the dynamic response and vibrational power flow in general three-dimensional coupled beam structures. An arbitrary loading condition is assumed and flexural waves in two perpendicular planes and longitudinal and torsional waves, may be excited simultaneously in each beam. The interaction of different wave types at the coupling boundaries is therefore expected. Suitable for the low- and medium-frequency range, the modal receptance method used here allows the prediction of the detailed structural response and power flow components carried by the different wave types through joint boundaries and at any cross section of the beam structure. The mathematical description of the three-dimensional beam structure and the manipulation of receptance matrices are presented in such a form that the vibration of any complex beam structure may be described systematically and with clear physical interpretations. The prediction of the input and output power for each component beam quantifies the energy dissipation in the beam, which may be taken as a measure of the spatial average response level of the beam. Computational examples of the power flow components at the joint boundaries of the component beams in coupled three-dimensional structures are used to illustrate the significance of the theoretical results.