An Approximate Theory for Elastic Wave Propagation in Multi-Bar Media.
Abstract
The phenomena of elastic wave propagation in prismatic bars is investigated by use of the approximate theories. In addition to several structural configurations that are synthesized from rectangular bar elements, the free bar and a single rectangular bar with mass distributed over several faces are considered. The first-order approximate theory of elastic wave propagation, when applied to bar elements, results in a twelve component displacement field in irreducible triplicates of motion, when the product series of Legendre polynomials in the lateral coordinates are truncated at first order. New results in the frequency spectra are presented for each of the irreducible triplicates of motion for bars experiencing free motion. Frequency spectra are presented for rectangular bars with mass distributions on its lateral faces. The presence of the mass was found to lead in some cases to more coupling between the modes of propagation. Finally, a structural configuration is synthesized with five rectangular bar elements, each of different material but perfectly bonded together. The first order theory is applied to obtain the equations of motion for each bar, which are then coupled together through the equality of certain forces and displacements at the interfaces. Numerical results in the form of frequency spectra are presented for two and three bar configurations. The spectra demonsteate that it is possible to duplicate the behavior expected from a higher order approximate theory by use of the first order approximate theory with a sufficient number of finite bar elements. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1970
- Accession Number
- AD0732233
Entities
People
- James E. Wade
Organizations
- Air Force Institute of Technology