Vibrations of Elastic Plates

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. - 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. - 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. Language: English