Publication Cover
Applicable Analysis
An International Journal
Volume 78, 2001 - Issue 1-2
24
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Analysis of the solvability of a model for the vibration of a damaged beam

&
Pages 9-20 | Received 01 Jan 2000, Published online: 02 May 2007

References

  • Viljoen , H.J. and Rensburg , N.F.J. 04,1996 . Damage detection in composites by ZnO sensors . AIChE Journal , 42 ( 2 ) : 1101 – 1107 .
  • Jooste , B.R. , Viljoen , H.J. , Rohde , S.L. and van Rensburg , N.F.J. 05/06,1996 . Experimental and theoretical study of vibration of a cantilevered beam using a ZnO piezoelectric sensor . J Vac Sci Tech. A , 14 ( 3 ) : 714 – 719 .
  • Zietsman , L. and van Rensburg , N.F.J. 2000 . A numerical study of the vibrations of a damaged beam . Mathematical and Computer Modelling , 31 ( 6-7 ) : 51 – 60 .
  • Lax , P.D. and Milgram , A.N. 1954 . “ Parabolic equtions Contributions to the theory of partial differential equations ” . In Ann Math Studies , Vol. 33 , N.J : Princeton University Press .
  • Showalter , R. E. 1977 . “ Parabolic equtions Contributions to the theory of partial differential equations ” . In Hilbert space methods for partial differential equations , Pitman .
  • Krein , S.G. 1971 . Linear differential equations in Banach spaces, Translations of Mathematical Monographs . Amer Math Soc, Providence, R.I , 29
  • Fung , Y C. 1965 . Foundation of soild mechanics , Englewood Cliffs , New Jersey : Prentice-Hall Inc .
  • Inman , D. J. 1994 . Engineering vibration , Englewood Cliffs , New Jersey : Prentice-Hall Inc .
  • Banks , H.T. and Inman , D.J. 1991 . On damping mechanisms in beams . Transactions of the ASME, J Appl Mech , 58 : 716 – 723 .
  • Friedman , A. 1969 . Partial differential equationss , Vol. 1 , New York : Holt .
  • Oden , J.T. and Reddy , J.N. 1976 . “ An introduction to the mathematical theory of finite elements ” . John Wiley and Sons .
  • Pazy , A. 1983 . Semigroups of linear operators and applications to partial differential equations .
  • Rauch , J. 1985 . On convergence of the finite element method for the wave equations . SIAM J. Numer Anal , 22 ( 2 ) : 245 – 249 .
  • Zaidman , S.D. 1979 . “ Abstract differential equations ” . In pitman , Francisco , , London : Advanced Publishing Program .

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.