Curvature Effects on Vibrational Power Flow of Smooth Bent Beams

Abstract

This study discusses an approach to analyze curvature effects on the vibrational powerflow of slender beams. A finite element method (FEM) model was used to calculate transmitted and reflected power via the “propagating wave approach”. Previously, the same investigation was addressed with focus on the analytical formulation of curved beams, and an FEM model was programmed using simple two-node straight (Euler-Bernoulli) beam elements. However, the model could simulate in-plane vibrations only, with restrictions to high frequencies (lower than two wavelengths inside the curvatures length). Hence, a new model was proposed, and the curvature parametrization was updated. A novel method to parametrize the curvature in 3D is discussed using quaternions. Results from the updated FEM model and analytical approach were compared for validation. Moreover, the algorithm performed almost exactly like the analytical model, even at high frequencies, which made it suitable to simulate power flow based on the wave approach. The algorithm allows any type of curve configuration to be tested. Curvature effects for in- and out-of-plane vibrations are shown as well. Finally, this work introduces a basis for designing and optimizing slender pipe structures from the perspective of vibration control.