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TECHNICAL PAPERS

Free Response of Twisted Plates with Fixed Support Separation

[+] Author and Article Information
Eric M. Mockensturm

Department of Mechanical & Nuclear Engineering, Pennsylvania State University, University Park, Pa 16802

C. D. Mote

University of Maryland, College Park, MD 20742

J. Vib. Acoust 123(2), 175-180 (Sep 01, 2000) (6 pages) doi:10.1115/1.1340626 History: Received October 01, 1999; Revised September 01, 2000
Copyright © 2001 by ASME
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References

Thomson, W. (Lord Kelvin), and Tait, P. G., 1883, Treatise of Natural Philosophy, Cambridge University Press, London.
de Saint-Venant, A., 1855, “De la Torsion des Prismes, avec des considérations sur leur Flexion,” Mémoires des Savants Étrangers.
Green,  A. E., 1936, “The Equilibrium and Elastic Stability of a Thin Twisted Strip,” Proc. R. Soc. London, Ser. A, 125, pp. 430–455.
Green,  A. E., 1937, “The Elastic Stability of a Thin Twisted Strip-II,” Proc. R. Soc. London, Ser. A, 161, pp. 197–220.
Reissner,  E., 1957, “Finite Twisting and Bending of Thin Rectangular Plates,” ASME J. Appl. Mech., 24, pp. 391–396.
Reissner,  E., and Wan,  F., 1968, “On Axial Extension and Torsion of Helicoidal Shells,” J. Math. Phys., 47, pp. 1–31.
Chen,  C. H. S., 1974, “Finite Twisting and Bending of Thin Rectangular Orthotropic Elastic Plates,” ASME J. Appl. Mech., 41, pp. 315–316.
Wan, F., 1990, “Finite Axial Extension and Torsion of Elastic Helicoidal Shells,” Asymptotic and Computational Analysis, R. Wong, ed., Marcel Dekker, New York & Basel, pp. 491–516.
Reissner,  E., 1992, “A Note on Finite Twisting and Transverse Bending of Shear Deformable Orthotropic Plates,” Int. J. Solids Struct., 29, p. 2177–2180.
Reissner,  E., 1992, “On the Finite Twisting and Bending of Non-Homogeneous, Anisotropic Elastic Plates,” ASME J. Appl. Mech., 59, pp. 1036–1038.
Crispino,  D. J., and Benson,  R. C., 1986, “Stability of Twisted Orthotropic Plates,” Int. J. Solids Struct., 28, pp. 371–379.
Mockensturm,  E. M., and Mote,  C. D., 1999, “Steady Motions of Translating, Twisted Webs,” Int. J. Non-Linear Mech., 34, pp. 247–257.
Casey,  J., 1992, “On Infinitesimal Deformation Measures,” J. Elast., 28, pp. 257–269.
Naghdi, P. M., 1972, “The Theory of Shells and Plates,” S. Flügge’s Handbuch der Physik, C. Truesdell, ed., Vol. VIa/2, Springer-Verlag, Berlin, pp. 425–633.
Naghdi, P. M., 1980, “Finite Deformation of Elastic Rods and Shells,” Proceedings of the IUTAM Symposium on Finite Elasticity, D. E. Carlson and R. T. Shield, eds., Vol. 47, pp. 47–103.

Figures

Grahic Jump Location
The reference, equilibrium, and present configurations of a twisted plate. Coordinates ψi are convected with the plate.
Grahic Jump Location
Natural frequencies of the plate with n=1,T⁁=100, ε=1/5000, and η=1 (even mode dashed, odd mode solid)
Grahic Jump Location
Natural frequencies of the plate with n=1,T⁁=100, ε=1/500, η=1 (even mode dashed, odd mode solid)
Grahic Jump Location
Natural frequencies of the plate with n=1,T⁁=0, ε=1/5000, η=1 (even mode dashed, odd mode solid)
Grahic Jump Location
Natural frequencies of the plate with n=1,T⁁=1000, ε=1/5000, η=1 (even mode dashed, odd mode solid)
Grahic Jump Location
Natural frequencies of the plate with n=1,T⁁=100, ε=1/5000, and ã=0.15 (even mode dashed, odd mode solid)
Grahic Jump Location
Natural frequencies of the plate with n=1,T⁁=100,ã=0.15, η=1 (even mode dashed, odd mode solid)
Grahic Jump Location
Natural frequencies of the plate with n=1, ε=1/5000, ã=0.18, η=1 (even mode dashed, odd mode solid)

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