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The analysis of internally supported thin plates by the boundary element method. Part 2 - Free vibration analysis

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Abstrakty
EN
A free vibration analysis of internally supported Kirchhoff plates 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 [26], [31], [32], [34]. Two unknown and independent variables have been considered at the boundary element node. The Bettie theorem has been used to derive the boundary integral equation. The collocation version of boundary element method with elements of "constant" type has been presented. The source points are located slightly outside the plate boundary, hence the quasi-diagonal integrals of fundamental functions are non-singular [27], [31], [32], [34].
Rocznik
Tom
Strony
43--74
Opis fizyczny
Bibliogr. 34 poz.
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autor
autor
Bibliografia
  • 1. Brebbia C.A., Telles J.C.F. and Wróbel L.C.: Boundary Element Techniques, Theory and Applications in Engineering, Springer-Yerlag, Berlin Heidelberg, New York, Tokyo, 1984.
  • 2. Burczyński T.: The Boundary Element Method in Mechanies, Technical--Scientific Publishing house, Warszawa, 1995 (in Polish).
  • 3. Timoshenko S., Woinowsky-Krieger S.: Theory of plates and shells, Arkady, Warszawa, 1962.
  • 4. Nadai A.: Uber dic Biegung durchlaufender Platten und der rechtcckigen Platte mit frcicn Randern, Zeitschritt fur angewandtc Mathematik und Mechanik, 2, 1922.
  • 5. Iguchi S.: Dic Eingenschwingungcn und Klangfiguren der Klangfiguren der viersciting freien rcchtcckigen Platte, Ingenicur-Archiv, 21 (1953), 5-6.
  • 6. Nishimura T.: Studiem on vibration problcms of flat plater by mcans of dif-ference calculus, Proceedings Third Japancsc National Congress of Applied Mechanies, 1953.
  • 7. Kaczkowski Z.: Orthotropic rectangular plates with free edges, Archiwum Mechaniki Stosowanej, 7 (4) (1955) (in Polish).
  • 8. Cox, H.L. Boxer. J.: Yibration of rectangular plates point supported at the corners. Aeronautical Quartcrly, 11 (2) (1960).
  • 9. Johns D.J., Nagaraj V.T.: On thc fundamental frequcncy of a squarc plate symmctrically supported at four points, Journal of Sounds and Yibrations, 10 (3) (1969).
  • 10. Dowell E.H.: Free vibration of a linear structure with arbitrary supported condition, Journal of Applied Mechanies, ASME, 38 (3) (l 971).
  • 11. Mirza W.H., Petyt M.: On the vibration of point-supported plates, Journal of Sounds and Yibrations, 15 (3) (1971).
  • 12. Pctyt M., Mirza W.H.: Yibration of column-supported floor slabs, Journal of Sounds and Yibrations, 21 (3) (1971).
  • 13. Damie S.FC., Fceser L.J.: Yibration of four point supported plates by a finite element method, Journal of Aeronautical Society of India, 24, 1972.
  • 14. Yenkateswara Rao G., Raju I.S., Amba-Rao C.L.: Yibration of point-supported plates, Journal of Sounds and Yibrations, 25 (1) (l 973).
  • 15. Bezinc G.: Boundary integral formulation for piąte flexurc with arbitrary boundary condition, Mechanics Research Communications, 5(4) (1978), 197-206.
  • 16. Stern M.: A general boundary integral formulation for the numerical solution of piate bending problems, Int. J. Solids Structures 15 (1979), 169-782.
  • 17. Bezine G.: A boundary integral couation method for platc flexure with condition inside the domain, Int. J. Num. Meth. Engng. 15 (1981), 1647-1657.
  • 18. Yander Weeen F.: Application of the boundary integral equation method to Reissner's piąte model, Int. J. Num. Meth. Engng., 18 (1982) 1-10.
  • 19. de Paiva J.B., Ycnturini W.S.: Boundary element algorithm for building floor slab analysis, In International Conference of BETECH 85, Adelaide, Australia, Brebbia C.A., Noye B.J. (cds), Computational Mechanics Publications(1985),201-209.
  • 20. Harlmann F., Zotemantcl R.: The dircct boundary element method in plate bending, Int. J. Num. Meth. Engng., 23 (1986), 2049-2069.
  • 21. de Paiva J.B., Yenlurini W.S.: Analysis of building structures considering plate-beam-cohimn interactions, In International Conference of BETECH 87, Rio de Janeiro, Brazil, Brebbia C.A., Yenturini W.S. (cds), Computational Mechanics Publications (1987), 209-219.
  • 22. Abdel-Akher A., Hartlcy G. A.: Domain integration for plate bending analysis by the boundary element method, Applied Numerical Method, 5 (1989), 23-28.
  • 23. Abdel-Akher A., Hartley G. A.: Eyaluation of boundary integrals for plate bending. Int. J. Num. Meth. Engng., 28 (1989), 75-93.
  • 24. Katsikadclis J.T. Sapountzakis EJ., Zorba E.G.: A BEM approach to static and dynamic analysis of plates. Computational Mechanics, 7(1) (1990), 31--42.
  • 25. Shi G., Flexural vibration and buckling analysis of orthotropic plates by the boundary element method, International Journal of Solids Structures, 12 (26) (1990), 1351-1370.
  • 26. El-Zafrany A., Debbih M. and Fadhil S.: A modified Kirchhoff thcory for boundary element bonding analysis of thin plates, Int. J. Solids Structures, 21 (31) (1994), 2885-2889.
  • 27. Hartley G. A.: Development of piąte bending elements for frame analysis, Engineering Analysis with Boundary Element, 17, 2 (1997) 93-104.
  • 28. Providakis C.P., Toungelis G.: A D/BEM approach to the transient response analysis of elastoplastic plates, Engineering Computations, 5(4) (1998), 501-511.
  • 29. Litewka P., Sygulski R.: Static and dynamie analysis of bridge slabs by the fmite strip method, Archives of Civil Engineering XLV (2) (1999). 259--273.
  • 30. Rashed Y. F.: A coupled BEM-flexibility force method for bending analysis of internally supported plates. Int. J. Num. Meth. Engng., 54 (2002), 1431-1457.
  • 31. Guminiak M., Okupniak B., Sygulski R.: Analysis of piąte bending by boundary element method, 2nd European Conference on Computational Mechanics ECCM-2001, June 26-29, Cracow, Pofand, l, 2001, 176-177.
  • 32. Guminiak M.: Application of the boundary element method in static analysis of thin plates (in Polish), 3nd Scientific Conference of PhD Students of Civil Engineering, Gliwice-Wisla, 21-22 November, 2002, Silesian University of Technology, Poland, 223-232.
  • 33. Woźnica K.: Yibration and bending of rectangular plates supported punctu-ally (in Polish), PhD Thesis, Warsaw University of Technology, Faculty of Civil Engineering, 1978.
  • 34. 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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPP1-0077-0012
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