Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 11
40
Views
3
CrossRef citations to date
0
Altmetric
Articles

Harmonic vibration of prismatic shells in zero approximation of Vekua's hierarchical models

&
Pages 2275-2287 | Received 22 Aug 2012, Accepted 12 Sep 2012, Published online: 12 Oct 2012

References

  • Jaiani , G . 2011 . “ Cusped Shell-like Structures ” . In SpringerBriefs in Applied Science and Technology , Heidelberg, Dordrecht, London, New York : Springer .
  • Makhover , E . 1957 . Bending of a plate of variable thickness with a cusped edge . Scientific Notes Leningrad State Ped. Inst. , 17 ( 2 ) : 28 – 39 . (in Russian)
  • Mikhlin , SG . 1970 . Variational Methods in Mathematical Physics , Moscow : Nauka . (in Russian)
  • Jaiani , G . Cylindrical bending of a rectangular plate with power law changing stiffness, Proceedings of Conference of Young Scientists in Mathematics. Tbilisi University Press, 1976, pp. 49–52 (in Russian)
  • Jaiani , G . 1977 . On the bending of a plate with power law changing stiffness . Annuaire Ecoles Sup. Mech. Techn. , 12 ( 2 ) : 15 – 19 .
  • Khvoles , AR . 1971 . The general representation for solutions of equilibrium equations of prismatic shell with variable thickness . Semin. I. Vekua Inst. Appl. Math. Rep. Annot. Rep. , 5 : 19 – 21 . (in Russian)
  • Tsiskarishvili , GV and Khomasuridze , NG . 1991 . Axially symmetric strained state of a cusped conical and cylindrical shells . Proc. I. Vekua Inst. Appl. Math. , 42 : 59 – 71 . (in Georgian)
  • Tsiskarishvili , GV and Khomasuridze , NG . 1991 . Cylindrical bending of a cusped cylindrical shell . Proc. I. Vekua Inst. Appl. Math. , 42 : 72 – 79 .
  • Jaiani , G . 1992 . On some applications of variational methods in the bending theory of prismatic sharpened shells . Proc. I. Vekua Inst. Appl. Math. , 47 : 36 – 44 .
  • Devdariani , GG . 1992 . On the solution with finite energy for bending equation of the prismatic sharpened shell . Proc. I. Vekua Inst. Appl. Math. , 47 : 17 – 25 . (in Russian)
  • Jaiani , G . 2004 . Bending of a cusped plate on an elastic foundation . Bull. TICMI , 8 : 22 – 31 .
  • Chinchaladze , N . 2002 . Vibration of the plate with two cusped edges . Proc. I. Vekua Inst. Appl. Math. Tbilisi State Univ. , 52 : 30 – 48 .
  • Chinchaladze , N . 2008 . On some nonclassical problems for differential equations and their applications to the theory of cusped prismatic shells . Lecture Notes TICMI. , 9 : 1 – 92 .
  • Vekua , IN . 1955 . On a way of calculating of prismatic shells . Proc. A. Razmadze Inst. Math. Georgian Acad. Sci. , 21 : 191 – 259 . (in Russian)
  • Vekua , IN . 1985 . Shell Theory: General Methods of Construction , Pitman, Boston, London , , Melbourne : Pitman Advanced Publishing Program .
  • Chinchaladze , N , Jaiani , G , Gilbert , R , Kharibegashvili , S and Natroshvili , D . 2008 . Existence and uniqueness theorems for cusped prismatic shells in the N-th hierarchical model . Math. Methods Appl. Sci. , 31 ( 11 ) : 1345 – 1367 .
  • Jaiani , G , Kharibegashvili , S , Natroshvili , D and Wendland , WL . 2004 . Two-dimensional hierarchical models for prismatic shells with thickness vanishing at the boundary . J. Elasticity. , 77 ( 2 ) : 95 – 122 .
  • Jaiani , G and Schulze , B-W . 2007 . Some degenerate elliptic systems and applications to cusped plates . Math. Nachr. , 280 ( 4 ) : 388 – 407 .
  • Devdariani , G , Jaiani , G , Kharibegashvili , S and Natroshvili , D . 2000 . The first boundary value problem for the system of cusped prismatic shells in the first approximation . Appl. Math. Inform. , 5 ( 2 ) : 26 – 46 .
  • Vishik , MI . 1954 . Boundary value problems for elliptic equations degenerating of the boundary of domain . Math. Sb. 35 , 77 ( 3 ) : 513 – 568 . (in Russian)
  • Nikolskii , SM , Lizorkin , PI and Miroshin , NV . 1988 . Weighted functional spaces and their applications to the investigation of boundary value problems for degenerate elliptic equations . Izv. Vyssh. Ucheb. Zav. , 8 ( 315 ) : 4 – 30 .
  • Triebel , H . 1978 . Interpolation Theory Function Spaces, Differential Operators , Berlin : DVW .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.