Vibration of an elastic plate under action of an incompressible fluid in case ofN = 0 approximation of I. Vekua's hierarchical models

International Journal of Phytoremediation

Volumn 85, Issue 9, 2006, Pages 1177-1187

  Chinchaladze, N B ^a   Gilbert, R P ^b  

^a TBILISI STATE UNIVERSITY   (Georgia)

^b UNIVERSITY OF DELAWARE   (United States)

Author keywords

35Q72; 74H45; 74K20; Hierarchical models; Incompressible fluid; Interaction problem; MSC 2000: 74F10; Plates

Indexed keywords

EID: 70449695719     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810600835334     Document Type: Article

References (33)

1. Babuška, I, and Li, L. 1991. Hierarchic modelling of plates. Computers and Structures, 40: 419–430.
2. Bielak, J, and MacCamy, R. 1991. Symmetric finite element and boundary integral coupling methods for fluid-solid interaction. Quarterly of Applied Mathematics, 49: 107–119.
3. Buchanan, J, and Gilbert, RP. 1990. A solution of the equations of elastic shell theory. Mathematical Methods in the applied Sciences, 12: 341–363.
4. Chinchaladze, N. 2002. Bending of an isotropic cusped elastic plates under action of an incompressible fluid. Reports of Seminar of I. Vekua Institute of Applied Mathematics of Tbilisi State University, 28: 52–60.
5. Chinchaladze, N, and Jaiani, G. 2001. On a cusped elastic solid-fluid interaction problem. Applied Mathematics and Informatics, 6 (2): 25–64.
6. Chinchaladze, N. 2002. On a cusped elastic solid-incompressible fluid interaction problem. Harmonic vibration. Mechanics and Mechanical Engineering, Technical University of Lodz, 6: 5–29.
7. Chinchaladze, N. 2002. A cusped elastic plate-ideal incompressible fluid interaction problem. Reports of Seminar of I. Vekua Institute of Applied Mathematics of Tbilisi State University, 28: 31–39.
8. Chinchaladze, N, and Gilbert, R. Cylindrical vibration of an elastic cusped plate under action of an incompressible fluid in case ofN = 0 approximation of I.Vekua's hierarchical models. Complex Variables, 50 (7–11) 479–496.
9. Dautray, R, and Lions, JL. 1990. Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1, Berlin, Heidelberdg, New York, London, Paris, Tokyo, Hong Kong: Springer-Verlag.
10. Ershov, N. 1985. “ Solution of a three-dimensional diffraction problem of acoustic waves by potential method ”. In Mathematical Problems of Geophysics, Novosibirsk 47–58. (in Russian)
11. Everstine, G, and Au-Yang, M. 1984. Advances in Fluid-Structure Interaction, New York: American Socity of Mechanical Engineers.
12. Everstine, G, and Henderson, F. 1990. Coupled finite element/boundary element approach for fluid-structure interaction. Journal of the Acoustic Society of America, 87: 1938–1947.
13. Gilbert, R.P, and Wendland, W. 1974–1975. Generalized hyperanalytic systems with analytic coefficients,. Procedings of Society of Edinburgh73A, 22: 317–331.
14. Gilbert, RP, Scotti, T, Wirgin, A, and Xu, YS. 1998. The unidentified object problem in a shallow ocean. Journal of the Acoustic Society of America, 103: 1320–1327.
15. Gordeziani, DG. 1974. To the exactness of one variant of the theory of thin shells. Soviet. Math. Dokl., 215 (4): 751–754.
16. Jaiani, GV. 2004. Mechanics of Continuous Bodies, Tbilisi: Tbilisi University Press) (in Georgian).
17. Jaiani, GV. 1980. On a physical interpretation of Fichera's function. Acad. Naz. dei Lincei, Rend.della Sc.Fis.Mat.e Nat., S. VIII, Vol. LXVIII, fasc., 5: 426–435.
18. Jaiani, GV. 1999. “ Initial and boundary value problems for singular differential equations and applications to the theory of cusped bars and plates ”. In Complex Methods for Partial Differential Equations, Edited by: Begehr, H, Celebi, O, and Tutschke, W. Vol. 6, 113–149. Dordrecht: ISAAC Serials, (Kluwer).
19. Jaiani, GV. 2002. Relation of hierarchical models of cusped elastic plates and beams to the three-dimensional models. Reports of the Seminar of I.Vekua Institute of Applied Mathematics, 28: 40–51.
20. Jaiani, GV, Kharibegashvili, SS, Natroshvili, D.G, and Wendland, W.L. “ Hierarchical models for elastic cusped plates and beams ”. In Lecture Notes of TICMI (electronic version: http://www.viam.hepi.edu.ge/others/TICMI)
21. Jentsch, L, and Natroshvili, D. 1997. Interaction between thermoelastic and scalar oscillation fields. Integral Equations and Operator Theory, 28: 261–288.
22. Junger, MC, and Fiet, D. 1986. Sound, Structures and Their Interaction, Cambridge, MA: MIT Press.
23. Hsiao, GC. 1994. “ On the boundary-field equation methods for fluid-structure interactions ”. In Proceedings of the 10.TMP, Teubner Texte zur Mathematik, Bd, Vol 134, 79–88. Stuttgart-Leipzig.
24. Meunargia, TV. 1998. On nonlinear and nonshallow shells. Bulletin of TICMI, 2: 46–49.
25. Natroshvili, D, Kharibegashvili, S, and Tediashvili, Z. 2000. Direct and inverse fluid-structure interaction problems. Rendiconti di Matematica, Serie VII, 20: 57–92. Roma
26. Natroshvili, D, and Sadunishvili, G. 1996. Interaction of elastic and scalar fields. Mathematical Methods Applied Sciences, 19 (18): 1445–1469.
27. Obolashvili, E. 2003. Higher Order Partial Differential Equations in Clifford Analysis. Effective Solutions to Problems, Boston-Basel-Berlin: Birkhäuser.
28. Sanchez-Palencia, E. 1984. Non-homogeneous media and vibration theory. Moscow, Mir 1984, (in Russian)
29. Schwab, C. 1996. A-posteriori modelling error estimation for hierarchic plate models. Numerische Mathematik, 74: 221–259.
30. Vekua, I.N. 1965. The theory of thin shallow shells of variable thickness. Proceedings of A. Razmadze Institute of Mathematics of Georgian Academy of Sciences, 30: 5–103. (in Russian)
31. Vekua, IN. 1985. Shell Theory: General Methods of Construction. (Pitman Advanced Publishing Program, Boston-London-Melbourne), Boston-London-Melbourne: (Pitman Advanced Publisher Program).
32. Wol'mir, A. 1981. Shells on the Flow Fluid and Gas. Problems of Aero-elasticity, Moscow (in Russian).
33. Wol'mir, A. 1981. “ Shells on the Flow Fluid and Gas ”. In Problems of Hydro-elasticity Moscow (in Russian)