Solving direct and inverse problems of plate vibration by using the Trefftz functions

• Autorzy: Maciąg A. , Pawińska A.
• Języki publikacji: EN

Abstrakty

EN

The paper presents an approximate method of solving direct and inverse problems which are described by a non-homogenous plate vibration equation. The key idea of the presented approach is to use solving polynomials that satisfy the considered homogenous differentia equation identically. Inhomogeneity is expanded into the Taylor series and then, for each monomial, the inverse operator is calculated. In the paper, the properties of solving functions are investigated – a theorem concerning their linear independence is formulated and proved. The method of identification of the load (source) is described. It belongs to the group of inverse problems. The paper includes examples which illustrate the usefulness of the method.

Słowa kluczowe

EN

plate vibration; Trefftz method; inverse problem; source identification

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2013
• Tom: Vol. 51 nr 3
• Strony: 543--552
• Opis fizyczny: Bibliogr. 21 poz., rys., tab.

Twórcy

autor

Maciąg A.

• Kielce University of Technology, Faculty of Management and Computer Modelling, Kielce, Poland

autor

Pawińska A.

• Kielce University of Technology, Faculty of Management and Computer Modelling, Kielce, Poland

Bibliografia

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• 4. Grysa K., 2010, Trefftz Functions and their Applications in Solving the Inverse Problems, Kielce University of Technology Publishers [in Polish]
• 5. Grysa K., Maciąg A., 2011, Solving direct and inverse thermoelasticity problems by means of Trefftz base functions for finite element method, Journal of Thermal Stresses, 34, 4, 378-393
• 6. Kołodziej J.A., Zieliński A.P., 2009, Boundary Collocation Techniques and their Application in Engineering, WIT Press, Southampton, Boston
• 7. Li Z.-C., Qiu Lu T.-T., Hu H.-Y., Cheng H.-D., 2008, The Trefftz and Collocation Methods, WIT Press, Southampton, Boston
• 8. Maciąg A., 2004, Solution of the three-dimensional wave equation by using wave polynomials, PAMM – Proceedings in Applied Mathematics and Mechanics, 4, 706-707
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• 11. Maciąg A., 2009, Trefftz Functions for Some Direct and Invers Problems of Mechanics, Kielce University of Technology Publishers [in Polish]
• 12. Maciąg A., 2011a, The usage of wave polynomials in solving direct and inverse problems for two-dimensional wave equation. International Journal for Numerical Methods in Biomedical Engineering, 27, 1107-1125
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