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Vibrations of Elastic Plates Linear and Nonlinear Dynamical Modeling of Sandwiches, Laminated Composites, and Piezoelectric Layers

This book is based on my experiences as a teacher and as a researcher for more than four decades. When I started teaching in the early 1950s, I became interested in the vibrations of plates and shells. Soon after I joined the Polytechnic Institute of Brooklyn as a professor, I began working busily o...

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Bibliographic Details
Main Author: Yu, Yi-Yuan
Format: eBook
Language:English
Published: New York, NY Springer New York 1996, 1996
Edition:1st ed. 1996
Subjects:
Buildings / Design And Construction
Building Construction And Design
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 10.3 Classical Equations for Large Deflections of a Piezoelectric Plate
  • 10.4 Refined Equations for Large Deflections of a Piezoelectric Plate
  • 10.5 Final Remarks on the Variational Equations of Motion
  • References
  • 5.1 Classical Equations of a Laminated Composite Plate
  • 5.2 Refined Equations of a Laminated Composite Plate
  • 5.3 Flexural Vibration of a Symmetric Laminate: Useful Ranges of Equations
  • 5.4 Extensional Vibration of a Symmetric Laminate: Useful Ranges of Equations
  • References
  • 6 Linear Vibrations Based on Plate Equations
  • 6.1 Free Flexural Vibration of Plates with Simply Supported Edges
  • 6.2 Free Flexural Vibration of Plates with Clamped Edges
  • 6.3 Forced Flexural Vibration of Homogeneous and Sandwich Plates in Plane Strain
  • References
  • 7 Nonlinear Modeling for Large Deflections of Beams, Plates, and Shallow Shells
  • 7.1 Equations for Large Deflections of a Buckled Timoshenko Beam
  • 7.2 Von Kármán Equations for Large Deflections of a Plate: Incorporation of Transverse Shear Effect
  • 7.3 Marguerre Equations for Large Deflections of a Shallow Shell: Incorporation of Transverse Shear Effect
  • 7.4 Remarks on the Variational Equations of Motion
  • References
  • 8 Nonlinear Modeling and Vibrations of Sandwiches and Laminated Composites
  • 8.1 Equations for Large Deflections of a Sandwich Plate
  • 8.2 Nonlinear Vibration of a Sandwich Plate
  • 8.3 Equations for Large Deflections of a Laminated Composite Plate
  • 8.4 Nonlinear Vibration of an Orthotropic Symmetric Laminate
  • 8.5 Equations for Large Deflections of a Sandwich Beam with Laminated Composite Facings and an Orthotropic Core
  • References
  • 9 Chaotic Vibrations of Beams
  • 9.1 A Numerical Study of Chaos According to Duffing’s Equation: Effect of Damping
  • 9.2 More Poincaré Maps According to Duffing’s Equation for Small Damping
  • 9.3 Spectral Analysis of Chaos
  • 9.4 Acoustic Radiation from Chaotic Vibrations of a Beam.-References
  • 10 Nonlinear Modeling of Piezoelectric Plates
  • 10.1 From Elasticity to Peizoelectricity
  • 10.2 Generalized Hamilton’s Principle and Variational Equation of Motion Including Piezoelectric Effect
  • 1 Nonlinear Elasticity Theory
  • 1.1 Strains
  • 1.2 Stresses
  • 1.3 Strain Energy Function and Principle of Virtual Work
  • 1.4 Hamilton’s Principle and Variational Equations of Motion
  • 1.5 Pseudo-Variational Equations of Motion
  • 1.6 Generalized Hamilton’s Principle and Variational Equation of Motion
  • 1.7 Stress-Strain Relations in Nonlinear Elasticity
  • References
  • 2 Linear Vibrations of Plates Based on Elasticity Theory
  • 2.1 Equations of Linear Elasticity Theory
  • 2.2 Rayleigh-Lamb Solution for Plane-Strain Modes of Vibration in an Infinite Plate
  • 2.3 Simple Thickness Modes in an Infinite Plate
  • 2.4 Horizontal Shear Modes in an Infinite Plate
  • 2.5 Modes in an Infinite Plate Involving Phase Reversals in Both x-and y-Directions
  • 2.6 Plane-Strain Modes in an Infinite Sandwich Plate
  • 2.7 Simple Thickness Modes in an Infinite Sandwich Plate
  • References
  • 3 Linear Modeling of Homogeneous Plates
  • 3.1 Classical Equations for Flexure of a Homogeneous Plate
  • 3.2 Refined Equations for Flexure of an Isotropic Plate: Mindlin Plate Equations and Timoshenko Beam Equations
  • 3.3 Classical Equations for Extension of an Isotropic Plate
  • 3.4 Refined Equations for Extension of an Isotropic Plate
  • 3.5 Vibrations of an Infinite Plate: Useful Ranges of Plate Equations
  • 3.6 General Equations of an Anisotropic Plate
  • References
  • 4 Linear Modeling of Sandwich Plates
  • 4.1 Refined Equations for Flexure of a Sandwich Plate Including Transverse Shear Effects in All Layers
  • 4.2 Simplified Refined Equations for Flexure of a Sandwich Plate with Membrane Facings
  • 4.3 Classical Equations for Flexure of a Sandwich Plate
  • 4.4 Flexural Vibration of an Infinite Sandwich Plate: Useful Ranges of Sandwich Plate Equations
  • 4.5 Extensional Vibration of an Infinite Sandwich Plate Based onClassical Equations
  • References
  • 5 Linear Modeling of Laminated Composite Plates

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