The free vibrations analysis of plates resting on continuous internal supports by the boundary element method

• Autorzy: Guminiak M. , Sumelka W.
• Języki publikacji: EN

Abstrakty

EN

A free vibration analysis of Kirchhoff plates resting on continuous internal supports has been presented in the paper. Using the proposed approach, there is no need to introduce Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary. Two unknown and independent variables are considered at the boundary element node. The Bcttie theorem has been used to create the boundary integral equation. The collocation version of boundary element method with "constant" type of elements has been presented. The source points are located slightly outside the plate boundary, hence the quasi-diagonal integrals of fundamental functions are non-singular.

Słowa kluczowe

EN

boundary element method; Kirchhoff plates; fundamental solution; free vibration

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Civil and Environmental Engineering
• Rocznik: 2007
• Tom: No. 10
• Strony: 69--97
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Guminiak M.

autor

Sumelka W.

• Institute of Structural Engineering, Piotrowo 5, 61-138 Poznań Tel.: [phone]; fax: [phone],

Bibliografia

• 1. Woźnica K.: Vibration and bending of rectangular plates supported punctually (in Polish), PhD Thesis, Warsaw University of Technology, Faculty of Civil Engineering, 1978.
• 2. Guminiak M, Sygulski R.: The analysis of internally supported thin plates by the boundary element method. Part 1 - Static analysis. Foundation of Civil and Environmental Engineering, 9, (2007), 17-41.
• 3. Guminiak M, Sygulski R.: The analysis of internally supported thin plates by the boundary element method. Part 2 - Free vibration analysis. Foundation of Civil and Environmental Engineering, 9, (2007), 43-74.
• 4. Brebbia C.A., Telles J.C.F. and Wróbel L.C.: Boundary Element Techniques, Theory and Applications in Engineering, Springer-Verlag, Berlin Heidelberg, New York, Tokyo, 1984.
• 5. Burczyński T.: The Boundary Element Method in Mechanics, Technical-Scientific Publishing house, Warszawa, 1995 (in Polish).
• 6. Bezine G.: A boundary integral equation method for plate flexure with condition inside the domain, Int. J. Num. Meth. Engng. 15 (1981), 1647-1657.
• 7. Katsikadelis J.T. Sapountzakis E.J., Zorba E.G.: A BEM approach to static and dynamic analysis of plates. Computational Mechanics, 7(1) (1990), 31--42.
• 8. Providakis C.P., Toungelis G.: A D/BEM approach to the transient response analysis of elastoplastic plates, Engineering Computations, 5(4) (1998), 501
• 9. Rashed Y. F.: A coupled BEM-flexibility force method for bending analysis ot internally supported plates. Int. J. Num. Meth. Engng., 54 (2002), 1431
• 10. Shi G.: Flexural vibration and buckling analysis of orthotropic plates by the boundary element method, International Journal of Solids Structures, 12
• 11. Guminiak M.: Thin plates analysis by the boundary element method using new formulation of a boundary condition (in Polish), PhD Thesis Poznań University of Technology, Poznań, Poland, 2004.
• 12. Hartley G. A.: Development of plate bending elements for frame analysis Engineering Analysis with Boundary Element, 17, 2 (1997) 93-104.