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Nonlinear Modeling and Vibrations of Sandwiches and Laminated Composites

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Vibrations of Elastic Plates

Abstract

In the preceding chapter, a method of developing nonlinear dynamical models has been applied to homogeneous beams, plates, and shallow shells through the use of a pseudo-variational equation of motion in nonlinear elasticity. The famous Timoshenko beam equations, von Kármán plate equations, and Marguerre shallow shell equations have been rederived and extended. In this chapter, the method is further applied to layered plates, including sandwiches and laminated composites. The equations derived are next applied to the analysis of nonlinear vibrations.

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References

  • Hyer, M.W., W.J. Anderson, and R.A. Scott. (1976) Nonlinear Vibrations of Three-Layer Beams of Viscoelastic Cores—I. Theory. Journal of Sound and Vibrations, Vol. 46, pp. 121–136.

    Article  MATH  Google Scholar 

  • Hyer, M.W., W.J. Anderson, and R.A. Scott. (1978) Nonlinear Vibrations of Three-Layer Beams of Viscoelastic Cores—II. Experiment. Journal of Sound and Vibrations, Vol. 61, pp. 25–30.

    Article  Google Scholar 

  • Kovac, E.J., Jr., W.J. Anderson, and R.A. Scott. (1971) Forced Nonlinear Vibration of a Damped Sandwich Beam. Journal of Sound and Vibrations, Vol. 17, pp. 25–39.

    Article  MATH  Google Scholar 

  • Wu, C.I. and J.R. Vinson. (1969) On the Nonlinear Oscillations of Plates Composed of Composite Materials. Journal of Composite Materials, Vol. 3, pp. 548–561.

    Article  Google Scholar 

  • Yu, Y.Y (1959a) A New Theory of Elastic Sandwich Plates—One-Dimensional Case. Journal of Applied Mechanics, Vol. 26, pp. 415–421.

    MATH  Google Scholar 

  • Yu, Y.Y. (1959b) Simple Thickness-Shear Modes of Vibration of Infinite Sandwich Plates. Journal of Applied Mechanics, Vol. 26, pp. 679–681.

    Google Scholar 

  • Yu, Y.Y. (1962) Nonlinear Flexural Vibrations of Sandwich Plates. Journal of the Acoustical Society of America, Vol. 34, pp. 1176–1183.

    Article  Google Scholar 

  • Yu, Y.Y (1963) Application of Variational Equation of Motion to the Nonlinear Vibration Analysis of Homogeneous and Layered Plates and Shells. Journal of Applied Mechanics, Vol. 30, pp. 79–86.

    Google Scholar 

  • Yu, Y.Y. (1989) Dynamics and Vibration of Layered Plates and Shells—A Perspective from Sandwiches to Laminated Composites. Bound volume for the 30th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, pp. 2236–2245.

    Google Scholar 

  • Yu, Y.Y. (1991) Nonlinear Dynamics and Chaos of Buckled Sandwich Beams with Isotropic or Laminated Composite Facings. In: Proceedings of the Eighth International Conference for Composite Materials, pp. 3-D-1 to 3-D-15.

    Google Scholar 

  • Yu, Y.Y. (1992a) Dynamics and Vibration of Layered Plates and Shells—A Perspective from Sandwiches to Laminated Composites. Russian translation. In: Mechanics of Composite Materials, Vol. 2, Construction of Composites, Proceedings of the First Soviet-American Symposium, pp. 99–108. Riga, Latvia.

    Google Scholar 

  • Yu, Y.Y. (1992b) Equations for Large Deflections of Homogeneous and Layered Beams with Application to Chaos and Acoustic Radiation. Composites Engineering, Vol. 2, pp. 117–136.

    Article  MATH  Google Scholar 

  • Yu, Y.Y. (1992c) Equations for Large Deflections of Elastic and Piezoelectric Plates and Shallow Shells, Including Sandwiches and Laminated Composites, with Applications to Vibrations, Chaos, and Acoustical Radiation. Presented at the XIIIth International Congress of Theoretical and Applied Mechanics, Haifa, Israel.

    Google Scholar 

  • Yu, Y.Y. (1992d) 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.

    Google Scholar 

  • Yu, Y.Y. (1993) Nonlinear Large-Deflection Vibrations of Laminated Composite Plates. In: Proceedings of the 8th Technical Conference on Composite Materials, American Society for Composites, pp. 1099–1108. Technomic Publishing Co., Lancaster, Pennsylvania.

    Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

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© 1996 Springer-Verlag New York, Inc.

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Yu, YY. (1996). Nonlinear Modeling and Vibrations of Sandwiches and Laminated Composites. In: Vibrations of Elastic Plates. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2338-2_8

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  • DOI: https://doi.org/10.1007/978-1-4612-2338-2_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7509-1

  • Online ISBN: 978-1-4612-2338-2

  • eBook Packages: Springer Book Archive

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