Green's function for vibration problems of an elliptical membrane

• Autorzy: Kukla S.
• Języki publikacji: EN

Abstrakty

EN

The aim of the paper is to derive the Green's function of the Helmholtz operator in an elliptical region. The function is found in the form of a double series of Mathieu functions, which are obtained as a solution to the associated boundary problem. The Dirichlet condition on the boundary ellipse is assumed. The eigenvalues are the roots of characteristic equations, which are derived from the boundary condition. To construct Green's function depending on time, the orthogonality condition of the eigenfunctions in the elliptical region was used.

Słowa kluczowe

EN

Green's functions; elliptic membrane; vibrations

PL

funkcja Greena; membrana eliptyczna; drgania

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2011
• Tom: Vol. 10, nr 2
• Strony: 129--134
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Kukla S.

• Institute of Mathematics, Czestochowa University of Technology, Poland,

Bibliografia

• [1] Chatjigeorgiou I.K., The analytic form of Green’s function in elliptic coordinates, Journal of Engineering Mathematics 2011, 1-19.
• [2] Gutierrez-Vega J.C., Rodriguez-Dagnino R.M., Meneses-Nava M.A., Chavez-Cerda S., Mathieu functions, a visual approach, American Journal of Physics 2003, 71(3), 233-242.
• [3] Hasheminejad S.M., Rezaei S., Hosseini P., Exact solution for dynamic response of an elastic elliptical membrane, Thin-Walled Structures 2011,49, 371-378.
• [4] Kukla S., Method of fundamental solutions for Helmholtz eigenvalue problems in elliptical domains, Scientific Research of the Institute of Mathematics and Computer Science 2009, 1(8), 85--90.
• [5] Kang S.W., Lee M.J., Kang Y.J., Vibration analysis of .arbitrarily shaped membranes using nondimensional dynamic influence function, Journal of Sound and Vibration 1999, 221(1), 117-132.
• [6] Duffy D.G., Green’s functions with applications, Chapman & Hall/CRC, Boca Raton, Washington DC 2001.
• [7] Kukla S., Funkcje Greena i ich zastosowania, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2009.