Curvature effects of vibrational power flow through Euler-Bernoulli beams

Paulo Victor Ribeiro Martins¹; Arcanjo Lenzi¹

¹ UFSC

doi:10.20906/CPS/COB-2015-1973

Resumo

The scope of this project is to analyze curvature effects on vibrations, e.g. the vibrational power flow changes through a smooth bend in the plane of curvature. This phenomenon is particularly of interest since extensional and transversal waves are coupled. In addition, the parametrization of this phenomena is relatively complex due to the dependency on two non-related constants, i.e. the radius and bend angle. This paper starts with a brief literature review on the works of Walsh & White (1999), Wu & Lundberg (1995) and Kang, and Riedel & Tan (2002). The (non-dimensional) parametrization differs in literature; this work therefore discusses a suitable set of non-dimensional parameters for algebraic simplifications. Thereafter, this work presents the equations of motion of an Euler-Bernoulli's curved beam. Moreover, it analytically examines the coupling between extensional and transversal waves, and the differences of straight and curved wavenumbers. Finally, equations for transmission and reflection coefficients were derived with the wave propagation approach. The results depict the effects of curvature on transmission and reflection coefficients. Two cases were considered, e.g. deviating bend angles with constant radius, and varying radii with constant bend angle.

Palavras-chave: curvature; wavenumber; power flow; Euler-Bernoulli; propagation