Elastic Wave Propagation in an Infinite Bar of Elliptical Cross Section

Abstract

This paper studies harmonic wave propagation in an infinite elastic bar of elliptical cross section with stress-free surface by using Mathieu functions and modified Mathieu functions which are the exact solutions of the equation of motion from linear elasticity in an elliptical cylinder coordinate system. We give a procedure leading to the frequency equations for longitudinal, torsional and flexural waves by making use of the orthogonal properties of Mathieu functions. Numerical calculation for each mode is carried out.