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Vibrations of Elastic Plates Yi-Yuan Yu

Vibrations of Elastic Plates By Yi-Yuan Yu

Vibrations of Elastic Plates by Yi-Yuan Yu


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Summary

Soon after I joined the Polytechnic Institute of Brooklyn as a professor, I began working busily on my research in vibrations of sandwich and layered plates and shells, and then teaching a graduate course on the same subject.

Vibrations of Elastic Plates Summary

Vibrations of Elastic Plates: Linear and Nonlinear Dynamical Modeling of Sandwiches, Laminated Composites, and Piezoelectric Layers by Yi-Yuan Yu

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 on my research in vibrations of sandwich and layered plates and shells, and then teaching a graduate course on the same subject. Although I tried to put together my lecture notes into a book, I never finished it. Many years later, I came to the New Jersey Institute of Technology as the dean of engineering. When I went back to teaching and looked for some research areas to work on, I came upon laminated composites and piezoelectric layers, which appeared to be natural extensions of sandwiches. Working on these for the last several years has brought me a great deal of joy, since I still am able to find my work relevant. At least I can claim that I still am pursuing life-long learning as it is advocated by educators all over the country. This book is based on the research results I accumulated during these two periods of my work, the first on vibrations and dynamical model ing of sandwiches, and the second on laminated composites and piezoelec tric layers.

Table of Contents

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 on Classical 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 Karman 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 Poincare 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.

Additional information

NPB9780387945149
9780387945149
0387945148
Vibrations of Elastic Plates: Linear and Nonlinear Dynamical Modeling of Sandwiches, Laminated Composites, and Piezoelectric Layers by Yi-Yuan Yu
New
Hardback
Springer-Verlag New York Inc.
1996-04-25
228
N/A
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