Abstract
Helical structures are designed to support heavy loads, which can significantly affect the dynamic behaviour. This paper proposes a physical analysis of the effect of axial load on the propagation of elastic waves in helical beams. The model is based on the equations of motion of loaded helical Timoshenko beams. An eigensystem is obtained through a Fourier transform along the axis. The equations are made dimensionless for beams of circular cross-section and the number of parameters governing the problem is reduced to four (helix angle, helix index, Poisson coefficient, and axial strain). A parametric study is conducted. The effect of loading is quantified in high, medium and low-frequency ranges. Noting that the effect is significant in low frequencies, dispersion curves of stretched and compressed helical beams are presented for different helix angles and radii. This effect is greater as the helix angle increases. Both the effects of stress and geometry deformation are shown to be non-negligible on elastic wave propagation.
Highlights
Helical structures are used in many engineering applications
The aim of this paper is to investigate the effect of axial loads on the propagation of guided modes in helical waveguides
The effect of load on the wave propagation is studied in each frequency range
Summary
Helical structures are used in many engineering applications. Typical examples are helical springs, widely used in automotive and aeronautic industry, and steel multi wire cables, largely encountered in civil engineering. In [16], a semi analytical finite element method has been proposed for the analysis of guided wave propagation inside multi wire helical waveguides, typically encountered in civil engineering. These studies neglect the presence of applied loads, whose effect remains unexplored on guided waves. Multi wire waveguides are not considered and the model is based on the equations of motion of Timoshenko loaded helical beams Such a model is not valid at high frequencies, when high order modes become propagating, but constitutes a first step and can serve as a reference solution before the development of fully three dimensional models, as done in [14 16] without loads.
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