Linear and Nonlinear Structural Mechanics

by Nayfeh, Ali H.; Pai, P. Frank

• ISBN13: 9780471593560
• ISBN10: 0471593567
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-07-16
• Publisher: Wiley-VCH

Summary

'ˆ— Explains the physical meaning of linear and nonlinear structural mechanics. 'ˆ— Shows how to perform nonlinear structural analysis. 'ˆ— Points out important nonlinear structural dynamics behaviors. 'ˆ— Provides ready-to-use governing equations.

Author Biography

ALI H. NAYFEH received his BS in engineering science and his MS and PhD in aeronautics and astronautics from Stanford University. He holds honorary doctorates from Marine Technical University, Russia, Technical University of Munich, Germany, and Politechnika Szczecinska, Poland. He is currently University Distinguished Professor of Engineering at Virginia Tech. He is the Editor of the Wiley Series in Nonlinear Science and Editor in Chief of Nonlinear Dynamics and the Journal of Vibration and Control.<br> <br> PERNGJIN FRANK PAI received his PhD in engineering mechanics from Virginia Polytechnic Institute and State University. He is the C. W. LaPierre Professor of Mechanical and Aerospace Engineering at the University of Missouri-Columbia. His research concentrates on highly flexible deployable/inflatable structures, structural damage detection, and nonlinear finite elements.

Table of Contents

Preface.

1. Introduction.

1.1 Structural Elements.

1.2 Nonlinearities.

1.3 Composite Materials.

1.4 Damping.

1.5 Dynamic Characteristics of Linear Discrete Systems.

1.6 Dynamic Characteristics of Nonlinear Discrete Systems

1.7 Analyses of Linear Continuous Systems.

1.8 Analyses of Nonlinear Continuous Systems.

2. Elasticity.

2.1 Principles of Dynamics.

2.2 Strain-Displacement Relations.

2.3 Transformation of Strains and Stresses.

2.4 Stress-Strain Relations.

2.5 Governing Equations.

3. Strings and Cables.

3.1 Modeling of Taut Strings.

3.2 Reduction of String Model to Two Equations.

3.3 Nonlinear Response of Strings.

3.4 Modeling of Cables.

3.5 Reduction of Cable Model to Two Equations.

3.6 Natural Frequencies and Modes of Cables.

3.7 Discretization of the Cable Equations.

3.8 Single-Mode Response with Direct Approach.

3.9 Single-Mode Response with Discretization Approach.

3.10 Extensional Bars.

4. Beams.

4.1 Introduction.

4.2 Linear Euler-Bernoulli Beam Theory.

4.3 Linear Shear-Deformable Beam Theories.

4.4 Mathematics for Nonlinear Modeling.

4.5 Nonlinear 2-D Euler-Bernoulli Beam Theory.

4.6 Nonlinear 3-D Euler-Bernoulli Beam Theory.

4.7 Nonlinear 3-D Curved Beam Theory Accounting for Warpings.

5. Dynamics of Beams.

5.1 Parametrically Excited Cantilever Beams.

5.2 Transversely Excited Cantilever Beams.

5.3 Clamped-Clamped Buckled Beams.

5.4 Microbeams.

6. Surface Analysis.

6.1 Initial Curvatures.

6.2 Inplane Strains and Deformed Curvatures.

6.3 Orthogonal Virtual Rotations.

6.4 Variation of Curvatures.

6.5 Local Displacements and Jaumann Strains.

7. Plates.

7.1 Introduction.

7.2 Linear Classical Plate Theory.

7.3 Linear Shear-Deformable Plate Theories.

7.4 Nonlinear Classical Plate Theory.

7.5 Nonlinear Modeling of Rectangular Surfaces.

7.6 General Nonlinear Classical Plate Theory.

7.7 Nonlinear Shear-Deformable Plate Theory.

7.8 Nonlinear Layerwise Shear-Deformable Plate Theory.

8. Dynamics of Plates.

8.1 Linear Vibrations of Rectangular Plates.

8.2 Linear Vibrations of Membranes.

8.3 Linear Vibrations of Circular and Annular Plates.

8.4 Nonlinear Vibrations of Circular and Annular Plates.

8.5 Nonlinear Vibrations of Rotating Disks.

8.6 Nonlinear Vibrations of Near-Square Plates.

8.7 Micropumps.

8.8 Thermally Loaded Plates.

9. Shells.

9.1 Introduction.

9.2 Linear Classical Shell Theory.

9.3 Linear Shear-Deformable Shell Theories.

9.4 Nonlinear Classical Theory for Double-Curved Shells.

9.5 Nonlinear Shear-Deformable Theories for Circular Cylindrical Shells.

9.6 Nonlinear Layerwise Shear-Deformable Shell Theory.

9.7 Nonlinear Dynamics of Infinitely Long Circular Cylindrical Shells.

9.8 Nonlinear Dynamics of Axisymmetric Motion of Closed Spherical Shells.

Bibliography.

Subject Index.