The Wkb Approximation and Periodicity Effects for Perturbed Helical Springs

Abstract eng:
Periodic curvature in rods exposed to time harmonic loads have previously been studied by [1] with the aim to design stop and pass bands filters of an elastic waveguide. The structure was composed of segments with constant curvature and which enable the determination of the dispersions relations by standard methods. The conclusion drawn is that a relatively large insertion loss may be obtained with proper choice of curvatures. In the approach taken in this work the curvature in each period are taken as varying and thus the wave propagation in each period may be determined by the use of the WKB approximation provided that the curvature is only slowly changing. The methodology is applied to problems of helical springs that have periods with gradually changing curvature, and the periodicity effects may consequently be studied by classical Floquet theory. This proposed analysis facilitates the choice of the optimal curvature since the impact if this is clearer due to the use of the WKB approximation.

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