Propagation of Harmonic Waves in an Elastic Rod of Elliptical Cross-Section

Author: Wong, Po Kee

Year: 1966

Degree: Engineer's thesis

Advisors: Miklowitz, Julius; Caughey, Thomas Kirk

Committee Member: Unknown, Unknown

Option: Mechanical Engineering

DOI: 10.7907/CX6S-JQ42

Abstract

Using the potential equations of motion of linear elasticity, the propagation of harmonic waves in an infinite rod of elliptical cross-section is investigated. The frequency equations for the propagation of flexural waves in rods with (i) zero surface displacements, and (ii) zero surface stresses are obtained in the form of infinite determinants, the elements of which involve Mathieu functions and their derivatives. It is shown that these determinants can be written in diagonal form when the eccentricity goes to zero and in the light of this possible numerical procedures are discussed for small values of the eccentricity.

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