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TECHNICAL PAPERS

Relationship Between Vibration Frequencies of Reddy and Kirchhoff Polygonal Plates With Simply Supported Edges

[+] Author and Article Information
C. M. Wang

Department of Civil Englneering, The National University of Singapore, Kent Ridge 119260, Singapore

S. Kitipornchai

Department of Civil Engineering, The University of Queensland, Brisbane 4072, Australia

J. N. Reddy

Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843-3123

J. Vib. Acoust 122(1), 77-81 (Oct 01, 1997) (5 pages) doi:10.1115/1.568438 History: Received July 01, 1996; Revised October 01, 1997
Copyright © 2000 by ASME
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References

Kirchhoff,  G., 1850, “Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe,” J. Angew. Math.,40, pp. 51–88.
Reissner,  E., 1944, “On the Theory of Bending of Elastic Plates,” J. Math. Phys., 23, pp. 184–191.
Reissner,  E., 1945, “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates,” ASME J. Appl. Mech., 12, pp. 69–77.
Hencky,  H., 1947, “Uber die Berucksichtigung der Schubverzerrung in ebenen Platten,” Ing. Arch.,16, pp. 72–76.
Mindlin,  R. D., 1951, “Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates,” ASME J. Appl. Mech., 18, pp. 31–38.
Wittrick,  W. H., 1973, “Shear Correction Factors for Orthotropic Laminates Under Static Load,” ASME J. Appl. Mech., 40, pp. 302–304.
Reddy,  J. N., 1984, “A Simple Higher-Order Theory for Laminated Composite Plates,” ASME J. Appl. Mech., 51, pp. 745–752.
Wang,  C. M., 1994, “Natural Frequencies Formula for Simply Supported Mindlin Plates,” ASME J. Vibr. Acoust.,116, pp. 536–540.
Wang,  C. M., 1996, “Vibration Frequencies of Simply Supported Polygonal Sandwich Plates via Kirchhoff Solutions,” J. Sound Vib., 190, pp. 255–260.
Reddy, J. N., 1997, Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton, Florida.
Reddy,  J. N., and Phan,  N. D., 1985, “Stability and Vibration of Isotropic, Orthotropic and Laminated Plates According to a Higher-Order Shear Deformation Theory,” J. Sound Vib., 98, pp. 157–170.
Reddy, J. N., 1999, Theory and Analysis of Elastic Plates, Taylor & Francis, Philadelphia, Pennsylvania.
Conway, H. D., 1960, “Analogies Between the Buckling and Vibration of Polygonal Plates and Membranes,” Canadian Aeronautical Journal, pp. 263.
Pnueli,  D., 1975, “Lower Bounds to the Gravest and All Higher Frequencies of Homogeneous Vibrating Plates of Arbitrary Shape,” ASME J. Appl. Mech., 42, pp. 815–820.
Leissa, A. W., 1993, Vibration of Plates, Edition by Acoustical Society of America (originally issued by NASA, 1969).

Figures

Grahic Jump Location
Comparison between Reddy and Kirchhoff vibration solutions

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