Thin-walled Laminated Structures (eBook)

Buckling, Vibrations and Their Suppression

Gennadi I. Mikhasev, Holm Altenbach (Autoren)

eBook Download: PDF

2019
X, 280 Seiten
Springer International Publishing (Verlag)
978-3-030-12761-9 (ISBN)

Infos

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.

 

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 29.4.2019
• Reihe/Serie: Advanced Structured Materials
• Reihe/Serie: Advanced Structured Materials
• Zusatzinfo: X, 280 p. 107 illus., 8 illus. in color.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: buckling analysis • Electrorheological Properties • Magnetorheological Properties • sandwich structures • Shell Structure • thin-walled structures • Vibration Supression • Viscoelastic Shells
• ISBN-10: 3-030-12761-3 / 3030127613
• ISBN-13: 978-3-030-12761-9 / 9783030127619