Abstract
In the remaining chapters in this book, we shall extend our treatment to nonlinear vibrations of thin structures that involve large deflections. Nonlinear dynamical modeling for such structures is introduced in the present chapter. This is followed in Chapter 8 with discussions of nonlinear vibrations of layered beams and plates, again including both sandwiches and laminated composites. Chaotic vibrations of elastic beams are then explored in Chapter 9. Finally, in Chapter 10, nonlinear dynamical modeling for large deflections of piezoelectric plates is treated.
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References
Chia, C.Y. (1980) Nonlinear Analysis of Plates. McGraw-Hill, New York.
Dym, C.L. and LH. Shames. (1973) Solid Mechanics: A Variational Approach. McGraw-Hill, New York.
Eringen, A.C. (1955) On the Nonlinear Oscillations of Viscoelastic Plates. Journal of Applied Mechanics, Vol. 22, pp. 563–567.
Fung, Y.C. (1965) Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, New Jersey.
Langhaar, H.L. (1962) Energy Methods in Applied Mechanics. Wiley, New York.
Marguerre, K. (1938) Zur Theorie Der Gekrummten Platte Grosser Formanderung. In: Proceedings of the 5th International Congress of Applied Mechanics, pp. 93–101.
Medwadowski, S.J. (1958) A Refined Theory of Elastic, Orthotropic Plates. Journal of Applied Mechanics, Vol. 25, pp. 437–443.
Novozhilov, V.V. (1948) Foundations of the Nonlinear Theory of Elasticity. (English translation, Graylock, Rochester, New York, 1953.)
Reddy, J.N. (1984) A Refined Nonlinear Theory of Plates with Transverse Shear Deformation. International Journal of Solids and Structures, Vol. 20, pp. 881–896.
Timoshenko, S. (1921) On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars. Philosophical Magazine, Series 6, Vol. 41, pp. 744–746.
Timoshenko, S. (1940) Theory of Plates and Shells, McGraw-Hill, New York.
Washizu, K. (1968) Variational Methods in Elasticity and Plasticity, Pergamon, New York (second edition, 1975; third edition, 1982).
von Kármán, T. (1910) Festigkeitsproblems im Maschinenbau. Encyklopadie der mathematischen Wissenschafter, Vol. 4, pp. 348–352.
Yu, Y.Y. (1963) Application of Variational Equation of Motion to the Nonlinear Analysis of Homogeneous and Layered Plates and Shells. Journal of Applied Mechanics, Vol. 30, pp. 79–86.
Yu, Y.Y. (1974) Application of Variational and Galerkin Equations to Linear and Nonlinear Finite Element Analysis. In: Proceedings of the 25th Congress of International Astronautical Federation, Amsterdam.
Yu, Y.Y. (1991) On Equations for Large Deflections of Elastic Plates and Shallow Shells. Mechanics Research Communications, Vol. 18, pp. 373–384.
Yu, Y.Y. (1992a) Equations for Large Deflections of Homogeneous and Layered Beams with Applications to Chaos and Acoustic Radiation. Composites Engineering, Vol. 2, pp. 117–136.
Yu, Y.Y. (1992b) Generalized Variational Equations of Motion in Nonlinear Anisotropic Elasticity and Plate Theories. In: Collection of Papers, a Volume Dedicated to the 80th Birthday of Academician V.V Novozhilov, edited by N.S. Solomenko, pp. 63–74. Shipbuilding Publishing House, St. Petersburg, Russia.
Yu, Y.Y. (1995a) On the Ordinary, Generalized, and Pseudo-Variational Equations of Motion in Nonlinear Elasticity, Piezoelectricity, and Classical Plate Theories. Journal of Applied Mechanics, Vol. 62, pp. 471–478.
Yu, Y.Y. (1995b) Some Recent Advances in Linear and Nonlinear Dynamical Modeling of Elastic and Piezoelectric Plates. Journal of Intelligent Material Systems and Structures, Vol. 6, pp. 237–254.
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© 1996 Springer-Verlag New York, Inc.
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Yu, YY. (1996). Nonlinear Modeling for Large Deflections of Beams, Plates, and Shallow Shells. In: Vibrations of Elastic Plates. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2338-2_7
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DOI: https://doi.org/10.1007/978-1-4612-2338-2_7
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