Root finding method for problems of elastodynamics

  • Anastasiya A. Krushynska Department of Natural Resources, Institute of Telecommunications and Global Information Space of the NAS Ukraine

Abstract

This paper presents a simple and efficient method for finding complex roots of dispersion equations occurring in many problems of elastodynamics. The method is characterized by high accuracy in root finding and absence of restrictions on function representation. The essence of the method is explained geometrically; initial guesses are found as the solutions to the appropriate problems of elastostatics. Numerical solutions to dispersion equations are obtained for two elastic isotropic waveguides: a plate of infinite cross-section and a rod of rectangular cross-section. For an infinite plate, the calculated results are in full conformity with those obtained by Newton-Raphson and bisection methods. For a waveguide of rectangular cross-section, the earlier unsolved problem of finding complex roots of dispersion equations is solved by the proposed method.

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Published
Jan 25, 2017
How to Cite
KRUSHYNSKA, Anastasiya A.. Root finding method for problems of elastodynamics. Computer Assisted Methods in Engineering and Science, [S.l.], v. 17, n. 1, p. 3–11, jan. 2017. ISSN 2299-3649. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/132>. Date accessed: 16 sep. 2021.
Section
Articles