Free vibration of thick generally laminated quadrilateral plates with point supports

37th AIAA/ASME/ASCE/AHS/ASC Structure, Structural Dynamics and Materials Conference

Volumn , Issue , 1996, Pages 248-258

  Lovejoy, Andrew E ^a   Kapania, Rakesh K ^a  

^a State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; LAMINATING; SHEAR DEFORMATION; STRESS-STRAIN CURVES; STRUCTURAL DYNAMICS; VIBRATIONS (MECHANICAL); APPROXIMATION THEORY; BOUNDARY CONDITIONS; FUNCTIONS; LAMINATED COMPOSITES; NUMERICAL METHODS; OPTIMIZATION; POLYNOMIALS; STRAIN; STRESSES;

ARTIFICIAL SPRINGS; CHEBYCHEV POLYNOMIALS; ESSENTIAL BOUNDARY CONDITIONS; FIRST-ORDER SHEAR DEFORMATION THEORY; FREE VIBRATION; LAMINATED PLATE; SIMPLY SUPPORTED; TRIAL FUNCTIONS;

PLATES (STRUCTURAL COMPONENTS);

ARTIFICIAL SPRINGS; CHEBYCHEV POLYNOMIALS; RAYLEIGH-RITZ METHOD; SHEAR CORRECTION;

EID: 0029699762     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.1996-1346     Document Type: Conference Paper

References (27)

1. Bhat, R. B., “Vibration of Rectangular Plates on Point and Line Supports Using Characteristic Orthogonal Polynomials in the Rayleigh-Ritz Method,” Journal of Sound and Vibration, Vol. 149, No. 1, 1991, pp. 170-172.
2. Gorman, D. J., “An Analytical Solution for the Free Vibration Analysis of Rectangular Plates Resting on Symmetrically Distributed Point Supports,” Journal of Sound and Vibration, Vol. 79, No. 4, 1981, pp. 561-574.
3. Gorman, D. J., “Free Vibration of Rectangular Plates with Symmetrically Distributed Point Supports Along the Edges,” Journal of Sound and Vibration, Vol. 73, No. 4, 1980, pp. 563-574.
4. Gorman, D. J., “A Note on the Free Vibration of Rectangular Plates Resting on Symmetrically Distributed Point Supports,” Journal of Sound and Vibration, Vol. 131, No. 3, 1989, pp. 515-519.
5. Raju, I. S., and Amba-Rao, C. L., “Free Vibrations of a Square Plate Symmetrically Supported at Four Points on the Diagonal,” Journal of Sound and Vibration, Vol. 90, No. 2, 1983, pp. 291-297.
6. Bapat, A. V., and Suryanarayan, S., “The Fictitious Foundation Approach to Vibration Analysis of Plates with Interior Point Supports,” Journal of Sound and Vibration, Vol. 155, No. 2, 1992, pp. 325-341.
7. Bapat, A. V., and Suryanarayan, S., “Free Vibrations of Periodically Point-Supported Rectangular Plates,” Journal of Sound and Vibration, Vol. 155, No. 2, 1992, pp. 325-341.
8. Bapat, A. V., and Suryanarayan, S., “Free Vibration of Rectangular Plates with Interior Point Supports,” Journal of Sound and Vibration, Vol. 134, No. 2, 1989, pp. 291-313.
9. Bapat, A. V., Venkatramani, N., and Suryanarayan, S., “A New Approach for the Representation of a Point Support in the Analysis of Plates,” Journal of Sound andVibration, Vol. 120, No. 1, 1988, pp. 107-125.
10. Kerstens, J. G. M, Laura, P. A. A., Grossi, R. O., and Ercoli, L., “Vibrations of Rectangular Plates with Point Supports: Comparison of Results,” Journal of Sound and Vibration, Vol. 89, No. 2, 1983, pp. 291-293.
11. Narita, Y., “The Effect of Point Constraints on Transverse Vibration of Cantilever Plates,” Journal of Sound and Vibration, Vol. 102, No. 3, 1985, pp. 305-313.
12. Saliba, H. T., “Experimental Free Vibration Analysis of Rectangular Cantilever Plates with Rigid Point Supports,” Journal of Sound and Vibration, Vol. 171, No. 4, 1994, pp. 459-472.
13. Saliba, H. T., “Free Vibration Analysis of Rectangular Cantilever Plates with Symmetrically Distributed Point Supports Along the Edges,” Journal of Sound and Vibration, Vol. 94, No. 3, 1984, pp. 381-395.
14. Mizusawa, T., and Kajita, T., “Vibration of Skew Plates Resting on Point Supports,” Journal of Sound and Vibration, Vol. 115, No. 2, 1987, pp. 243-251.
15. Aksu, G., and Felemban, M. B., “Frequency Analysis of Corner Point Supported Mindlin Plates by a Finite Difference Energy Method,” Journal of Sound and Vibration, Vol. 158, No. 3, 1992, pp. 531-544.
16. Kitipornchai, S., Xiang, Y., and Liew, K. M., “Vibration Analysis of Corner Supported Mindlin Plates of Arbitrary Shape Using the Lagrange Multiplier Method,” Journal of Sound and Vibration, Vol. 173, No. 4, 1994, pp. 457-470.
17. Srinivasan, R. S., and Munaswamy, K., “Frequency Analysis of Skew Orthotropic Point Supported Plates,” Journal of Sound and Vibration, Vol. 39, No. 2, 1975: 207-216.
18. Sadasiva Rao, Y. V. K., and Singh, G., “Vibration of Corner Supported Thick Composite Plates,” Journal of Sound and Vibration, Vol. 111, No. 3, 1986, pp. 510-514.
19. Li, N., and Gorman D. J., “Free Vibration Analysis of Clamped Rectangular Plates with Line Support Along Diagonals,” Journal of Sound and Vibration, Vol. 173, No. 5, 1994, pp. 591-598.
20. Li, N., and Gorman, D. J., “Free Vibration Analysis of Simply Supported Rectangular Plates with Internal Line Support Along Diagonals,” Journal of Sound and Vibration, Vol. 165, No. 2, 1993, pp. 361-368.
21. Kirn, C. S., and Dickinson, S. M., “The Flexural Vibration of Line Supported Rectangular Plate Systems,” Journal of Sound and Vibration, Vol. 114, No. 1, 1987, pp. 129-142.
22. Ding, Z., “Eigen frequencies of Line Supported Rectangular Plates,” International Journal of Solids and Structures, Vol. 31, No. 3, 1994, pp. 347-358.
23. Abrate, S., “Design of Multispan Composite Plates to Maximize the Fundamental Frequency,” Composites, Vol. 26, No. 10, 1995, pp. 691-697.
24. Lovejoy, A. E., and Kapania, R. K., “Natural Frequencies and an Atlas of Mode Shapes for Generally-Laminated, Thick, Skew, Trapezoidal Plates,” Center for Composite Materials and Structures, Virginia Polytechnic Institute and State University, Report 94-09, August 1994.
25. Lovejoy, A. E., and Kapania, R. K., “Natural Frequencies of Thick, Generally-Laminated, Skew; Trapezoidal, Cantilever Plates,” 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and AlAA/ASME Adaptive Structures Forum, AIAA 95-1350, Vol. 3, New Orleans, LA, April 10-13, 1995, pp. 1604-1618. To appear in AIAA Journal, July 1996.
26. Murti, V., and Valliappan, S., “Numerical Inverse Isoparametric Mapping in Remeshing and Nodal Quantity Contouring,” Computers and Structures, Vol. 22, No. 6, 1986, pp. 1011-1021.
27. Kapania, R. K., and Mohan, P., “Static, Free Vibration and Thermal Analysis of Composite Plates and Shells Using a Flat Triangular Shell Element,” To appear in Computational Mechanics, March 1996.