Symmetry in the problem of vibration of a polar-orthotropic non-homogeneous plate on an elastic foundation

Journal of Sound and Vibration

Volumn 201, Issue 3, 1997, Pages 365-381

  Klyachko, B ^a   Klyachko, S ^a  

^a Victorian Writers' Centre Inc   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

BENDING (DEFORMATION); COMPUTATIONAL METHODS; ELASTICITY; FOUNDATIONS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS; OPTIMIZATION; TENSORS; VIBRATIONS (MECHANICAL);

INVERSION TRANSFORMATION; POLAR ORTHOTROPIC NONHOMOGENEOUS ELASTIC PLATES; PROBLEM EQUATION INVARIANCE;

PLATES (STRUCTURAL COMPONENTS);

EID: 0031550997     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1996.0767     Document Type: Article

References (29)

1. J. H. MITCHELL 1902 Proceedings of the London Mathematical Society 34, 134-142. The inversion of plane stress.
2. J. H. MITCHELL 1902 Proceedings of the London Mathematical Society 34, 223-238. The flexure of a circular plate.
3. R. D. MINDLIN 1937 Journal of Applied Mechanics 4, A-115-A-118. Stress systems in a circular disk under radial forces.
4. W. OLSZAK and Z. MROZ 1957 Archiwum Mechaniki Stosowanej 9, 125-153. Elastic bending of circular plates with eccentric holes (application of the method of inversion).
5. W. OLSZAK 1958 Archiwum Mechaniki Stosowanej 10, 417-440. The inversion mapping as applied in the theory of plasticity.
6. V. T. BUCHVALD 1963 Mathematika (Journal of Pure and Applied Mathematics, London) 10, 29-34. Plane elastostatic boundary-value problems, part 2: the role of inversion.
7. S. D. KLYACHKO 1974 Journal of Applied Mechanics and Technical Physics 13, 250-252. Use of inversion transformation for modeling in certain problems of the theory of elasticity and plasticity. (New York: Consultants Bureau; translated from Russian).
8. H. P. W. GOTTLIEB 1991 Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics 58, 729-730. Inhomogeneous clamped circular plates with standard vibration spectra.
9. H. P. W. GOTTLIEB 1992 IMA Journal of Applied Mathematics 49, 185-192. Axisymmetric isospectral annular plates and membranes.
10. V. S. SARKISIAN 1976 Some Problems of the Mathematical Theory of Elasticity of Anisotropic Body. Erevan: Erevan University (in Russian).
11. S. ABRATE and E. FOSTER 1995 Journal of Sound and Vibration 179, 793-815. Vibrations of composite plates with intermediate line support.
12. K. M. LIEW and K. Y. LAM 1994 Journal of Sound and Vibration 174, 23-26. Effects of arbitrary distributed elastic point constraints on vibrational behaviour of rectangular plates.
13. R. Y. BODINE 1967 Journal of the Acoustical Society of America 41, 1551. Vibrations of a circular plate supported by a concentric ring of arbitrary radius.
14. V. X. KUNUKKASSERIL and A. S. J. SWAMIDAS 1974 International Journal of Solids and Structures 10, 603-619. Vibration of continuous circular plates.
15. Y. NARITA 1984 Journal of Sound and Vibration 93, 503-511. Variations of frequency parameters for plate with supporting location.
16. S. AZIMI 1988 Journal of Sound and Vibration 120, 37-52. Free vibration of circular plates with elastic or rigid interior supports.
17. C. S. KIM and S. M. DICKINSON 1989 Journal of Sound and Vibration 130, 363-377. On the lateral vibration of thin annular and circular composite plates subject to certain complicated effects.
18. T. S. SHIH and D. ALLAEI 1990 Journal of Sound and Vibration 140, 239-257. On the free vibration of annular plates with ring-type elastic attachments.
19. E. E. ALLEN 1954 Mathematical Tables and other Aids to Computation 8, 240-241. Analytical approximations.
20. E. E. ALLEN 1956 Mathematical Tables and other Aids to Computation 10, 162-164. Polynomial approximations to some modified Bessel functions.
21. M. ABRAMOWITZ and I. A. STEGUN 1964 Handbook of Mathematical Functions. Gaithersburg, MD: U.S. National Bureau of Standards.
22. S. M. VOGEL and D. W. SKINNER 1965 Transactions of the American Society of Mechanical Engineers (E), Journal of Applied Mechanics 32, 926-931. Natural frequencies of transversely vibrating uniform annular plates.
23. A. W. LEISSA 1969 Vibration of Plates. Washington, D.C.: NASA (Science paper SP-160).
24. R. LAL and U. S. GUPTA 1982 Journal of Sound and Vibration 83, 229-240. Axisymmetric vibrations of polar orthotropic annular plates of variable thickness.
25. J. B. GREENBERG and Y. STAVSKY 1979 Journal of the Acoustical Society of America 66, 501-508. Flexural vibrations of certain full and annular composite orthotropic plates.
26. E. WU and C.-S. YEN 1992 18th International Congress of Theoretical and Applied Mechanics Haifa, Israel, 159 Detection of impact force history and location on a laminated plate.
27. G. KEMPER 1974 Acustica 30, 173-179. The position dependence of the input power for point-shaped excited plate vibration.
28. Z. CELEP and D. TURHAN 1990 Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics 57, 677-681 Axisymmetric vibrations of circular plates on tensionless elastic foundations.
29. C. FANG and G. C. SPRINGER 1993 Journal of Composite Materials 27, 721-753. Design of composite laminates by a Monte Carlo method.