Solution of Transcendental and Algebraic Equations with Application to Wave Propagation in Elastic Plates.
Abstract
A numerical method is described by which theoretical formulas governing the propagation of symmetric and antisymmetric waves in elastic plate theory may be evaluated. Vital to evaluating the formulas is the availability of a means for solving transcendental equations. A generalized iterative rootfinder that was developed for this purpose is described. This rootfinder provides the investigator having access to computing facilities with a reliable means for solving transcendental equations. Dispersion curves for both the flexural and extensional waves in rubber, steel, and beryllium plates are calculated and plotted. These curves approach a real value k for the ratio of the Rayleigh to shear wave speeds. Values of this quantity calculated from the exact elasticity theory were compared with those obtained from an approximate formula given by Victorov. In addition, the inflection and the maximum points of the strain distribution throughout a free plate were calculated. It was found that inflection points in the strain distribution do not exist at all frequencies. In addition to a description and flow chart of the iterative rootfinder method, the significant graphs, equations, and computer programs that arose when computing the dispersion curve calculations are included. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 07, 1981
- Accession Number
- ADA103025
Entities
People
- C. M. Ruggiero
Organizations
- United States Naval Research Laboratory