Comparison of waveguide properties of curved versus straight planar elastic layers

Abstract

Dispersion equations are solved for the in-plane and anti-plane wave propagation in planar elastic layer with constant curvature. The classical Lamé formulation of displacements via elastic potentials is applied and appropriate simplifications are employed. The dispersion diagrams in each case are compared with their counterparts for a straight layer, e.g., the classical Rayleigh–Lamb solution. The curvature-induced symmetry-breaking effects are investigated for layers with symmetric boundary conditions. The role of curvature is also investigated in the cases, when the boundary conditions are not symmetrical. The elementary Bernoulli–Euler theory is employed to analyze the wave guide properties of a curved planar elastic beam in its in-plane deformation. The validity range of the Bernoulli–Euler theory is assessed via comparison of dispersion diagrams.