Qualitative theory in structural mechanics [electronic resource] : qualitative properties and existence of solutions / Dajun Wang, Qishen Wang, Beichang (Bert) He.
This book focuses on the qualitative theory in structural mechanics, an area that remains underdeveloped. The qualitative theory mainly deals with the static deformation and vibrational modes of linear elastic structures, and cover subjects such as qualitative properties and the existence of solutio...
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| Format: | Electronic eBook |
| Language: | English |
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Singapore :
Springer,
2019.
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Table of Contents:
- Intro; Preface; Contents; 1 Overview; 1.1 Brief History of the Development of the Qualitative Theory in Structural Mechanics; 1.2 Areas Covered in the Study of the Qualitative Theory in Structural Mechanics; 1.3 Key Theoretical Results and the Approach to Establish Them; 1.3.1 Oscillatory Properties in Static Deformation and Vibration of One-Dimensional Single-Span Structures; 1.3.2 Other Important Qualitative Properties; 1.3.3 Existence of Solutions in Structural Theories; 1.4 Theoretical and Practical Significance of the Qualitative Theory in Structural Mechanics.
- 1.4.1 Significance of Qualitative Properties of Structural Vibration and Static Deformation1.4.2 Significance of the Existence of Solutions in Structural Theories as Well as Other Subjects Within Fundamental Theories; 1.5 Overview of Qualitative Properties of Vibration Associated with Bars; 1.5.1 Qualitative Properties of Vibration Associated with the Continuous System of a Bar; 1.5.2 Qualitative Properties of Vibration of a Spring-Mass System; 1.5.3 Qualitative Properties of Vibration Associated with Other Discrete Systems of a Bar.
- 1.6 Overview of Qualitative Properties of Vibration Associated with Beams1.6.1 Qualitative Properties of Vibration Associated with the Continuous System of a Single-Span Beam; 1.6.2 Qualitative Properties of Vibration Associated with Continuous Systems of Overhang Beams; 1.6.3 Qualitative Properties of Vibration Associated with the Finite Difference System of a Beam; 1.6.4 Qualitative Properties of Vibration Associated with the Discrete System of a Multi-span Beam; 1.6.5 Qualitative Properties of Vibration Associated with Other Discrete Systems of a Beam.
- 1.7 Overview of Qualitative Properties of Vibration and Static Deformation Associated with Repetitive Structures1.7.1 Structures with Mirror Symmetry; 1.7.2 Rotationally and Linearly Periodic Structures; 1.7.3 Chain Structures; 1.7.4 Axisymmetric Structures; 1.8 Overview of the Existence of Solutions in Elasticity and Structural Theories as Well as Other Subjects in Fundamental Theories; 1.8.1 Types of Solutions in Elasticity and Structural Mechanics; 1.8.2 Existence Theorems for Solutions in Elasticity; 1.8.3 Existence Theorems for Solutions in Structural Theories.
- 1.8.4 Validity of Models of Structures in Structural TheoriesReferences; 2 Oscillatory Matrices and Kernels as Well as Properties of Eigenpairs; 2.1 A Few Notations and Definitions; 2.2 Some Relationship Among Minors; 2.3 Jacobian Matrix; 2.3.1 Jacobian Matrix and Sturm Sequence; 2.3.2 Eigenvalues and Eigenvectors of a Standard Jacobian Matrix; 2.3.3 The Concept of u-Lines and Their Nodes; 2.4 Oscillatory Matrices; 2.4.1 Definition of an Oscillatory Matrix and Its Identification Criteria; 2.4.2 Sign-Oscillatory Matrix; 2.4.3 Examples of Oscillatory and Sign-Oscillatory Matrices.