Free vibrations of rectangular cantilever plates. Part 1: Out-of-plane motion

Journal of Sound and Vibration

Volumn 271, Issue 1-2, 2004, Pages 131-146

  Seok, Jongwon ^a   Tiersten, H F ^a   Scarton, H A ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CANTILEVER BEAMS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; ELASTIC WAVES; ELASTICITY; PLATES (STRUCTURAL COMPONENTS);

CANTILEVER PLATES; TRANSCENDENTAL EQUATIONS;

VIBRATIONS (MECHANICAL);

EID: 1542473882     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-460X(03)00365-1     Document Type: Article

References (14)

1. A.W. Leissa, The free vibration of rectangular plates, Journal of Sound and Vibration 31 (3) (1973) 257-293.
2. S.F. Bassily, S.M. Dickinson, On the use of beam functions for problems of plates involving free edges, Journal of Applied Mechanics 42 (1975) 858-864.
3. R.B. Bhat, Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh-Ritz method, Journal of Sound and Vibration 102 (4) (1985) 493-499.
4. R.E. Rossi, P. A. A. Laura, Symmetric and antisymmetric normal modes of a cantilever rectangular plate: effect of Poisson's ratio and a concentrated mass, Journal of Sound and Vibration 195 (1) (1996) 142-148.
5. D.J. German, Free vibration analysis of cantilever plates by the method of superposition, Journal of Sound and Vibration 49 (4) (1976) 453-467.
6. D.J. Gorman, Accurate free vibration analysis of the orthotropic cantilever plate, Journal of Sound and Vibration 181 (4) (1995) 605-618.
7. R.D. Mindlin, An introduction to the mathematical theory of the vibration of elastic plates, US Army Signal Corps Engineering Laboratory, Fort Monmouth, NJ, Sec. 6.04, 1955.
8. P3/PATRAN™, User Manual Release 1.2, PDA Engineering-PATRAN Division, 1993.
9. (d), since it is for only one region.
10. F.B. Hildebrand, Methods of Applied Mathematics, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ, 1965, p. 219, Problem 100.
11. H.F. Tiersten, Linear Piezoelectric Plate Vibrations, Plenum Press, New York, 1969, Sec. 7.1.
12. Jongwon Seok, H.F. Tiersten, H.A. Scarton, Free vibrations of rectangular cantilever plates. Part 2: in-plane motion, Journal of Sound and Vibration 271 (1-2) (2004) 147-158, this issue.
13. Maple7trade;, User Manual Release 5, Waterloo Maple Inc., 1997.
14. D.C. Gazis, R.D. Mindlin, Extensional vibrations and waves in a circular disk and semi-infinite plate, Journal of Applied Mechanics 27 (1960) 541-547.