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Applicable Analysis
An International Journal
Volume 82, 2003 - Issue 7
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Original Articles

Analysis and Applications of Extended Kantorovich–Krylov Method

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Pages 713-740 | Received 15 Jan 2003, Published online: 17 Jan 2012

References

  • Bhat , R.B. , Singh , J. and Mundkur , G. 1993 . Plate characteristic functions and natural frequencies of vibration of plates by iterative reduction of partial differential equation . ASME Journal of Vibration and Acoustics , 115 ( 2 ) April : 177 – 181 .
  • Blevin , R.D. 1979 . Formulas for Natural Frequency and Mode Shape , New York : Van Nostrand Reinhold Company .
  • Chang , D.C. , Wang , G. and Wereley , N.M. 2002 . A generalized Kantorovich method and its application to free in-plane plate vibration problem . Applicable Analysis , 80 ( 3 ) : 493 – 523 .
  • Cortinez , V.H. and Laura , P.A.A. 1990 . Analysis of vibration rectangular plates of discontinuously varying thickness by means of the Kantorovich extended method . Journal of Sound and Vibration , 137 ( 3 ) : 457 – 461 .
  • Doyle , J. 1997 . Wave Propagation in Structures , New York : Spring-Verlag .
  • Evans , C. 1998 . “ Partial differential equations ” . In Graduate Studies in Mathematics , Vol. 19 , Providence , Rhode Island : American Mathematical Society .
  • Inma , D.J. 1994 . Engineering Vibration , Englewood Cliffs : Prentice Hall .
  • Kantorovich , L.V. and Krylov , V.I. 1964 . Approximate Methods of Higher Analysis , Groningen , , The Netherlands : Noordhoff .
  • Kerr , A.D. 1968 . An extension of Kantorovich method . Quarterly of Applied Mathematics , 26 ( 2 ) : 219 – 229 .
  • Kerr , A.D. and Alexander , H. 1968 . An application of the extended Kantorovich method to the stress analysis of a clamped rectangular plate . Acts Mechanica , 6 : 180 – 196 .
  • Kerr , A.D. 1969 . An extension of Kantorovich method for the solution of eigenvalue problems . International Journal of Solids and Structures , 5 : 559 – 572 .
  • Leissa , A. 1969 . Vibration of Plates , NASA SP-160 Washington , DC : U.S Government Printing Office .
  • Leissa , A. 1973 . The free vibration of rectangular plates . Journal of Sound and Vibration , 31 ( 3 ) : 257 – 293 .
  • Rajalingham , C. , Bhat , R.B. and Xistris , G.D. 1996 . Vibration of rectangular plates using plate characteristic functions as shape functions in the Rayleigh-Ritz method . Journal of Sound and Vibration , 193 ( 2 ) : 497 – 509 .
  • Rajalingham , C. , Bhat , R.B. and Xistris , G.D. 1996 . Closed form approximation of vibration modes of rectangular cantilevered plates by the variational reduced method . Journal of Sound and Vibration , 197 ( 3 ) : 263 – 281 .
  • Troutman , J.L. 1996 . Variational Calculus and Optimal Control , New York : Springer-Verlag .
  • Wang , G. , Veeramani , S. and Wereley , N.W. 2000 . Analysis of sandwich plates with isotropic face plates and a viscoelastic core . ASME Journal of Vibration and Acoustics , 122 ( 3 ) : 305 – 312 .
  • G. Wang (2001 December). Analyses of sandwich beams and plates structures with viscoelastic cores. Ph.D Dissertation, Dept. of Aerospace Engg., University of Maryland, College Park.
  • Wang , G. and Wereley , N.M. 2002 . Free in-plane vibration of rectangular plates . AIAA Journal , 40 ( 5 ) : 953 – 959 .
  • Wang , G. , Wereley , N.M. and Chang , D.C. 2003 . Analysis of sandwich plates with viscoelastic damping using two-dimensional plate modes . AIAA Journal , 41 ( 5 ) : 924 – 932 .

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