Ray and wave scattering in smoothly curved thin shell cylindrical ridges

TL;DR

This paper develops wave and ray models to analyze mid- and high-frequency vibrations in thin shell cylindrical ridges with smoothed joints, revealing how scattering properties change near the ring frequency.

Contribution

It introduces combined wave and ray approaches based on classical shell theory to study scattering in curved shell structures, focusing on the mid-frequency regime.

Findings

Ray model analyzed via phase-plane analysis revealing reflection and transmission properties.

Full wave scattering studied with finite difference method showing scattering behavior.

Identification of a qualitative change in wave dynamics near the ring frequency.

Abstract

We propose wave and ray approaches for modelling mid- and high- frequency structural vibrations through smoothed joints on thin shell cylindrical ridges. The models both emerge from a simplified classical shell theory setting. The ray model is analysed via an appropriate phase-plane analysis, from which the fixed points can be interpreted in terms of the reflection and transmission properties. The corresponding full wave scattering model is studied using the finite difference method to investigate the scattering properties of an incident plane wave. Through both models we uncover the scattering properties of smoothed joints in the interesting mid-frequency region close to the ring frequency, where there is a qualitative change in the dynamics from anisotropic to simple geodesic propagation.