Abstract：The six-order coupled differential equations are derived to describe the in-plane motion of thin, uniform, curved beam with constant curvature based on Flugge’s theory. The dispersion relationships and the ratios of tangential displacement to radial displacement for six wave components are obtained. Expressions for displacement, internal force and transformation matrices between physical domains and wave domains are derived. Energy transmission and reflection coefficients for coupled curved beam and semi-infinite straight beam are derived based on the wave propagation，reflection and transmission matrices. For a given incident extensional or flexural wave in the semi-infinite straight beam section, the relative energy flow of the reflected and transmitted waves of both kinds are determined as functions of frequency, curvature and bend angle. Numerical examples for energy transmission and reflection coefficients with different frequencies, different bend angles, different curvatures and different section dimensions are presented. Numerical results show that wave transmission and reflection by a curved beam introduces wave mode conversion, an incident wave of one type can induce reflected and transmitted waves of the other type; in the low frequency range, the wave mode conversion takes place for the reflected and transmitted wave; while, in the higher frequency range, the incident extensional or flexural wave can transmit without attenuation and conversion. In order to enhance the attenuation ability in the higher frequency range, curved beams with inserted single/multiple supports or vibration isolation masses are investigated. The simulation results show that the vibration isolation masses can impede wave propagation in the higher frequency range and the behavior of multiple vibration isolation masses with uniform distribution has band pass/stop characteristics usually demonstrated by periodic structures. This research provides qualitative guidelines for the design of curved beam structures.
2012, Vol. 31 
