HARMONIC WAVE PROPAGATION IN ELASTIC RODS OF ELLIPTICAL CROSS-SECTION.
Abstract
Using the potential equations of motion of linear elasticity, the propagation of harmonic waves in an infinite isotropic rod of elliptical cross-section is investigated. Three modes of motion are found to exist, corresponding to longitudinal, flexural, and torsional modes in a circular rod. The frequency equation for a flexural case is obtained in the form of an infinite determinant (set equal to zero), the elements of which involve Mathieu functions and their derivatives. It is shown that this determinant can be written in diagonal form when the eccentricity goes to zero, the diagonal elements describing the propagation of harmonic flexural and circumferential modes (of odd order) in a circular rod. Finally, some possible numerical procedures are discussed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1965
- Accession Number
- AD0625408
Entities
People
- J. Milowitz
- P. K. Wong
- R. A. Scott
Organizations
- California Institute of Technology