Energy flow analysis for curved beams

Abstract

This paper presents an energy model for the medium- and high-frequency analysis of Love–Kirchhoff curved beams. This model introduced by Nefske and Sung [Statistical Energy Analysis NCA 3, 47–54 (1987)] for straight beams and investigated further by other authors, is developed for curved rods (tangential or longitudinal waves), and then for curved beams (radial or flexural waves). The exact-energy solution for curved rods or beams is shown to consist of a smooth spatial variation, which the energy model represents, and a spatially oscillating solution, which can be represented by an energy envelope. Finally, a complete energy model is proposed for curved components including both longitudinal and flexural waves. Boundary conditions are also given in this paper. It is shown that this method, which is numerically attractive in the mid- and high-frequency range, predicts the arithmetic mean value of the energy variables.