Energy flow models for the out-of-plane vibration of horizontally curved beams

Abstract

The purpose of this work is to develop energy flow models to predict the out-of-plane vibration of horizontally curved beams in the mid- and high-frequency range. The dispersion relations of waves are approximately separated into relations to the propagation of flexural waves and torsional waves generating the out-of-plane vibration of the horizontally curved beams with Kirchhoff-Love hypotheses. The energy flow models are based on the energy governing equations for the flexural waves and the torsional waves propagating in the curved beams. Those equations are driven to predict the time- and locally space-averaged energy density and intensity in the curved beams. Total values for the energy density and the intensity as well as contributions of each type of waves on those values are predicted. A verification of the energy flow models for the out-of-plane vibration of the horizontally curved beams is performed by comparing the energy flow solutions for the energy density and the intensity with analytical solutions evaluated using the wave propagation approach. The comparison shows that the energy flow models can be effectively used to predict the out-of-plane vibration of the horizontally curved beams in the mid- and high-frequency range.