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Table of Contents
Intro
Preface
Introduction
Contents
1 Nanostructural Members in Various Fields: A Literature Review
1.1 Introduction
1.1.1 Nanobeams
1.1.2 Nanoplates
1.1.3 Nanoshells
References
2 Size-Dependent Theories of Beams, Plates and Shells
2.1 Introduction
2.2 Literature Review
2.3 Non-classical (Size-Dependent) Models of Beams, Plates and Shells
2.3.1 Nonlocal Theory
2.3.2 Modified Couple Stress Theory
2.3.3 Modified Theory of a Gradient of Deformations
2.3.4 Surface Theory of Elasticity
2.3.5 Size-Dependent Theory of Beams, Plates and Shells
2.3.6 Size-Dependent Theory of Beams, Plates and Shells Based on the Shear Deformations of the First Order Under the Timoshenko Theory (TBT)
2.3.7 Size-Dependent Theory of Beams, Plates and Shells Based on the Shear Deformation Model of the Third Order
2.3.8 Nonlocal HSDT-Based Models
References
3 Lyapunov Exponents and Methods of Their Analysis
3.1 Introduction
3.2 Largest Lyapunov Exponent (LLE)
3.3 Spectrum of Lyapunov Exponents
3.4 Benettin's Method ch33sps1
3.5 Wolf's Method ch33sps15
3.6 Rosenstein's Method ch33sps9
3.7 Kantz Method ch33sps6
3.8 Method Based on Jacobian Estimation ch33sps4,ch33sps10
3.9 Modification of the Neural Network Method ch32,ch33
References
4 Reliability of Chaotic Vibrations of Euler-Bernoulli Beams with Clearance
4.1 Introduction
4.2 Literature Review
4.3 Mathematical Model
4.4 Principal Component Analysis (PCA)
4.5 Numerical Experiment
4.6 Application of the Principal Component Analysis (PCA)
References
5 Analysis of Simple Nonlinear Dynamical Systems
5.1 Introduction
5.2 Gauss Wavelets ch55sps13
5.3 Logistic Map ch55sps10
5.4 Hénon Map ch55sps8
5.5 Hyperchaotic Generalized Hénon Map ch55sps9
5.6 Rössler Attractor ch55sps11
5.7 Lorenz Attractor ch55sps12
References
6 Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field
6.1 Introduction
6.2 Literature Review
6.3 Modified Couple Stress Theory of Thermoelastic Curvilinear Panels
6.4 Technical Theory for the Different Models
6.5 Static Solutions
6.6 Chaotic Dynamics of the Size-Dependent Flexible Beams
Preface
Introduction
Contents
1 Nanostructural Members in Various Fields: A Literature Review
1.1 Introduction
1.1.1 Nanobeams
1.1.2 Nanoplates
1.1.3 Nanoshells
References
2 Size-Dependent Theories of Beams, Plates and Shells
2.1 Introduction
2.2 Literature Review
2.3 Non-classical (Size-Dependent) Models of Beams, Plates and Shells
2.3.1 Nonlocal Theory
2.3.2 Modified Couple Stress Theory
2.3.3 Modified Theory of a Gradient of Deformations
2.3.4 Surface Theory of Elasticity
2.3.5 Size-Dependent Theory of Beams, Plates and Shells
2.3.6 Size-Dependent Theory of Beams, Plates and Shells Based on the Shear Deformations of the First Order Under the Timoshenko Theory (TBT)
2.3.7 Size-Dependent Theory of Beams, Plates and Shells Based on the Shear Deformation Model of the Third Order
2.3.8 Nonlocal HSDT-Based Models
References
3 Lyapunov Exponents and Methods of Their Analysis
3.1 Introduction
3.2 Largest Lyapunov Exponent (LLE)
3.3 Spectrum of Lyapunov Exponents
3.4 Benettin's Method ch33sps1
3.5 Wolf's Method ch33sps15
3.6 Rosenstein's Method ch33sps9
3.7 Kantz Method ch33sps6
3.8 Method Based on Jacobian Estimation ch33sps4,ch33sps10
3.9 Modification of the Neural Network Method ch32,ch33
References
4 Reliability of Chaotic Vibrations of Euler-Bernoulli Beams with Clearance
4.1 Introduction
4.2 Literature Review
4.3 Mathematical Model
4.4 Principal Component Analysis (PCA)
4.5 Numerical Experiment
4.6 Application of the Principal Component Analysis (PCA)
References
5 Analysis of Simple Nonlinear Dynamical Systems
5.1 Introduction
5.2 Gauss Wavelets ch55sps13
5.3 Logistic Map ch55sps10
5.4 Hénon Map ch55sps8
5.5 Hyperchaotic Generalized Hénon Map ch55sps9
5.6 Rössler Attractor ch55sps11
5.7 Lorenz Attractor ch55sps12
References
6 Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field
6.1 Introduction
6.2 Literature Review
6.3 Modified Couple Stress Theory of Thermoelastic Curvilinear Panels
6.4 Technical Theory for the Different Models
6.5 Static Solutions
6.6 Chaotic Dynamics of the Size-Dependent Flexible Beams