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 .