Mikhasev / Altenbach Thin-walled Laminated Structures

Buckling, Vibrations and Their Suppression
1. Auflage 2019
ISBN: 978-3-030-12761-9
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 106, 280 Seiten

Reihe: Advanced Structured Materials

This book presents a theoretical approach that allows the analysis of structures with magnetorheological and electrorheological layers, and shows, with the help of examples, how the mechanical behaviour of thin-walled laminated structures can be influenced.It consists of six chapters:Chapter 1 presents a brief overview of derivation approaches for theories of thin-walled structures, modelling of composites and modelling of laminated and sandwich structures.Chapter 2 describes the equivalent single layer model for thin laminated cylindrical shells, including the special cases of plates and beams. In addition to the classical mechanical properties, it also considers the electrorheological and magnetorheological properties.Chapter 3 presents the elastic buckling of laminated beams, plates, and cylindrical shells, discussing various problems, such as the influence of the boundary conditions, external loading and magnetic fields. It also suggests different approximations for asymptotic methods.Chapter 4 focuses on the free vibrations of elastic laminated beams, plates and cylindrical shells, investigating the influence of the boundary conditions and other factors.Chapter 5 presents the latest results concerning vibration of laminated structures composed of smart materials and discusses in detail the influence of electric and magnetic fields on smart structures. These results provide insights into the optimal design of these structures.Lastly, Chapter 6 features a short appendix presenting asymptotic estimates and series.  

Autoren/Hrsg.

Mikhasev, Gennadi I.

Altenbach, Holm

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Introduction;12
3.1;1.1 Derivation Approaches for Theories of Plates and Shells;12
3.2;1.2 Modeling of Composites;16
3.2.1;1.2.1 Preliminary Remarks and Definitions;17
3.2.2;1.2.2 Composite Materials;18
3.2.3;1.2.3 Volume Fibre Fraction;22
3.2.4;1.2.4 Modeling of Structures Composed of Composites;23
3.2.5;1.2.5 Material Characteristics of the Constituents;27
3.3;1.3 Modeling of Laminated Structures: Different Approaches;27
3.4;References;32
4;2 Equivalent Single Layer Model for Thin Laminated Cylindrical Shells;40
4.1;2.1 Equations of Thin Elastic Laminated Cylindrical Shells;40
4.1.1;2.1.1 Laminated Cylindrical Shell;41
4.1.2;2.1.2 Principal Hypotheses;42
4.1.3;2.1.3 Strain-displacement Relations;43
4.1.4;2.1.4 Constitutive Equations for Elastic Materials;44
4.1.5;2.1.5 Stress Resultants;45
4.1.6;2.1.6 Mixed Variational Principle;47
4.1.7;2.1.7 Equilibrium Equations and Natural Boundary Conditions;51
4.1.8;2.1.8 Transverse Shear Stresses and Their Resultants;53
4.1.9;2.1.9 Equations of Motion in Terms of Displacements;54
4.1.10;2.1.10 In-plane Stress State Equations;56
4.1.11;2.1.11 Technical Theory Equations;57
4.1.12;2.1.12 Error of Governing Equations;60
4.1.13;2.1.13 Displacement and Stress Function Boundary Conditions;61
4.1.14;2.1.14 Edge Effect Equations;65
4.1.15;2.1.15 Governing Equations for Laminated Plates and Beams;71
4.1.15.1;2.1.15.1 Laminated Plates;71
4.1.15.2;2.1.15.2 Laminated Beams;72
4.2;2.2 Governing Equations of Shell Buckling;72
4.2.1;2.2.1 Bending Stress State;73
4.2.2;2.2.2 In-plane Stress State;74
4.3;2.3 Laminated Cylindrical Shells with Viscoelastic Smart Layers;75
4.3.1;2.3.1 Viscoelastic Materials in Thin-walled Laminated Structures;76
4.3.2;2.3.2 Complex Moduli of Viscoelastic Materials;77
4.3.3;2.3.3 Smart Electro- and Magnetorheological Materials;78
4.3.3.1;2.3.3.1 Magnetorheological Elastomers;80
4.3.3.2;2.3.3.2 Electrorheological Composites;85
4.3.3.3;2.3.3.3 Magnetorheological Fluids;86
4.3.4;2.3.4 Governing Equations for Smart Cylindrical Shells;88
4.4;2.4 Finite Element Analysis;90
4.5;References;92
5;3 Elastic Buckling of Laminated Beams, Plates, and Cylindrical Shells;96
5.1;3.1 Simple Problems on Buckling of Laminated Beams and Plates;96
5.1.1;3.1.1 Laminated Beams;97
5.1.1.1;3.1.1.1 Simply Supported Beams;98
5.1.1.2;3.1.1.2 Simply Supported and Clamped Beams;100
5.1.2;3.1.2 Laminated Plates;101
5.1.2.1;3.1.2.1 Uniformly Loaded Edges;102
5.1.2.2;3.1.2.2 Non-uniformly Loaded Edges;102
5.2;3.2 Laminated Medium-length Cylindrical Shell Under External Pressure;103
5.2.1;3.2.1 Shell with Constant Parameters Under Uniform Pressure;105
5.2.1.1;3.2.1.1 Simply Supported Shell with Diaphragm on Edges;107
5.2.1.2;3.2.1.2 Effect of Shear on the Critical Buckling Pressure;109
5.2.1.3;3.2.1.3 Simply Supported Shell Without Diaphragm on Edges;111
5.2.2;3.2.2 Localized Forms of Buckling;122
5.2.2.1;3.2.2.1 Setting the Problem;123
5.2.2.2;3.2.2.2 Asymptotic Approach;124
5.2.2.3;3.2.2.3 Effect of Shears on Buckling Pressure and Localized Modes;132
5.3;3.3 Laminated Shell under Axial Compression;137
5.3.1;3.3.1 Circular Cylindrical Shell Under Uniform Axial Load;139
5.3.2;3.3.2 Classification of Buckling Modes;142
5.3.3;3.3.3 Non-Circular Cylinder Under Non-uniform Axial Load;145
5.3.3.1;3.3.3.1 Asymptotic Solution;146
5.3.3.2;3.3.3.2 Reconstruction of Asymptotic Expansions;151
5.3.4;3.3.4 Effect of Shear on Localized Buckling Modes and Critical Axial Force;154
5.4;3.4 Laminated Cylinder Under Torsion;157
5.4.1;3.4.1 Short Review of the State of the Art;158
5.4.2;3.4.2 Buckling Modes and Critical Torque;159
5.5;References;164
6;4 Free Vibrations of Elastic Laminated Beams, Plates and Cylindrical Shells;168
6.1;4.1 Laminated Beams;168
6.1.1;4.1.1 Governing Equation;170
6.1.2;4.1.2 Simply Supported Beam with Constant Parameters;171
6.1.3;4.1.3 Vibrations of Pre-stressed Beams on Elastic Foundation;172
6.2;4.2 Laminated Plates;178
6.2.1;4.2.1 Simply Supported Plate with Diaphragm on Edges;179
6.2.2;4.2.2 Simply Supported Plate Without Diaphragm on Edges;180
6.3;4.3 Simplest Problems on Free Vibrations of Thin Cylindrical Shells;184
6.3.1;4.3.1 Long Simply Supported Cylinder with Diaphragm on Edges;186
6.3.2;4.3.2 Medium-length Cylindrical Shells with Simply Supported Edges;189
6.3.2.1;4.3.2.1 Shell with Diaphragm on Edges: Solution in the Explicit Form;190
6.3.2.2;4.3.2.2 Shell without Diaphragm on Edges: Asymptotic Solution;190
6.4;4.4 Free Low-frequency Localized Vibrations of Medium-length Cylindrical Shells;194
6.5;4.5 Localized Vibrations of a Cylindrical Shell Pre-stressed by Distributed Axial Forces;198
6.5.1;4.5.1 Asymptotic Solution;199
6.5.2;4.5.2 Reconstruction of Asymptotic Solution;203
6.6;References;208
7;5 Vibrations of Laminated Structures Composed of Smart Materials;210
7.1;5.1 Brief Review of the State of the Art;211
7.2;5.2 Sandwich and Multi-layered Beams with Magnetorheological Core;214
7.2.1;5.2.1 Sandwich Beam with Magnetorheological Fluid Core;215
7.2.1.1;5.2.1.1 Free Vibrations;216
7.2.1.2;5.2.1.2 Forced Stationary Vibrations;218
7.2.1.3;5.2.1.3 Equivalent Model with External Friction for Prediction of Unsteady Vibrations;220
7.2.1.4;5.2.1.4 Suppression of Forced Vibrations in Thin-walled Structures via Magnetic/Electric Fields;222
7.2.1.5;5.2.1.5 High-frequency Response of Magnetorheological Beam on the Rapid Signal of a Magnetic Field;224
7.2.2;5.2.2 Laminated Beams with Magnetorhelogical Elastomer Layers;227
7.2.2.1;5.2.2.1 Free Vibrations;228
7.2.2.2;5.2.2.2 Forced Stationary Vibrations and Their Suppression;232
7.3;5.3 Magnetorheological Sandwich and Multi-Layered Plates;234
7.3.1;5.3.1 Free Vibrations;235
7.3.2;5.3.2 Forced Stationary Vibrations;236
7.4;5.4 Shells with Magneto- and Electrorhelogical Layers Affected by Magnetic/Electric Fields;237
7.4.1;5.4.1 Governing Equations and Boundary Conditions;238
7.4.2;5.4.2 Free Vibrations;240
7.4.2.1;5.4.2.1 Main Tunable Complex Parameters;242
7.4.2.2;5.4.2.2 Free Low-frequency Vibrations of Medium-length Cylindrical Sandwich Panels;247
7.4.3;5.4.3 Steady-state Forced Vibrations and Their Suppression;254
7.5;5.5 Influence of Stationary Magnetic Field on Localized Modes of Free Vibrations;259
7.5.1;5.5.1 Setting the Problem;259
7.5.2;5.5.2 Localized Natural Modes;261
7.5.2.1;5.5.2.1 Non-circular Cylinder;262
7.5.2.2;5.5.2.2 Circular Magnetorhelogical Elastomer-based Cylinder with Nonuniform Physical Properties;264
7.6;5.6 Suppression of Travelling Vibrations in Magnetorhelogical Elastomer-based Shells;266
7.6.1;5.6.1 Setting of the Initial Boundary Value Problem;266
7.6.2;5.6.2 Asymptotic Approach;268
7.6.2.1;5.6.2.1 Initial Boundary Value Problem for the jth Wave Packet;269
7.6.2.2;5.6.2.2 Sequence of One-dimensional Boundary Value Problems on Moving Generatrix;270
7.6.2.3;5.6.2.3 Zeroth-order Approximation;271
7.6.2.4;5.6.2.4 First-order Approximation;271
7.6.2.5;5.6.2.5 Second-order Approximation;272
7.6.2.6;5.6.2.6 Higher-order Approximations;273
7.6.3;5.6.3 Solution of the Initial Boundary Value Problem in the Leading Approximation;274
7.6.4;5.6.4 Running Localized Vibrations in Magnetorhelogical Elastomer-based Cylindrical Shells vs. Magnetic Field;275
7.6.4.1;5.6.4.1 Wave Packets in Shells with Constant Parameters;275
7.6.4.2;5.6.4.2 Wave Packets in Shells with Variable Geometrical Parameters;277
7.7;References;280
8;6 Appendix: Asymptotic Estimates and Series;284
8.1;6.1 Estimates of Functions;284
8.2;6.2 Asymptotic Series;285
8.3;References;286
9;Index;287