Wave polynomials for solving different types of two-dimensional wave equations
Abstract
The paper demonstrates a specific power series expansion technique used to obtain the approximate solution of the two-dimensional wave equation in some unusual cases. The solution for inhomogeneous wave equation, for more complicated shape geometry of the body, discrete boundary conditions and a membrane whose thickness is not constant is shown. As solving functions (Trefftz functions), so-called wave polynomials are used. Recurrent formulas for the particular solution are obtained. Some examples are included.
Keywords
wave equation, wave polynomials, Trefftz method, membrane vibrations,References
[1] E. Trefftz. Ein Gegenstük zum Ritzschen Verfahren. In: Proceedings 2nd International Congres of Applied Mechanics, 131-137, Zurich 1926.[2] A.P. Zieliński and I. Herrera. Trefftz method: fitting boundary conditions. Int. J. Num. Meth. Eng., 24: 871-891, 1987.
[3] P.C. Rosenbloom and D.V. Widder. Expansion in terms of heat polynomials and associated functions . Trans. Am. Math. Soc., 92: 220-266, 1956.
[4] H. Yano, S. Fukutani and A. Kieda. A boundary residual method with heat polynomials for solving unsteady heat conduction problems. Journal of the Franklin Institute, 316 (4): 291-298, 1983.
[5] S. Futakiewicz and L. Hożejowski. Heat polynomials method in the n-dimensional direct and inverse heat conduction problems. In: A.J. Nowak, C.A. Brebbia, R. Bielecki and M. Zerroukat, eds., Advanced Computational Method in Heat Transfer V, 103-112, Southampton UK and Boston USA: Computational Mechanics Publications 1998.
Published
Nov 21, 2022
How to Cite
MACIĄG, Artur; WAUER, Jörg.
Wave polynomials for solving different types of two-dimensional wave equations.
Computer Assisted Methods in Engineering and Science, [S.l.], v. 12, n. 4, p. 363-378, nov. 2022.
ISSN 2956-5839.
Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/972>. Date accessed: 13 nov. 2024.
Issue
Section
Articles
