- 结构力学中的定性理论--解的定性性质与存在性/高瞻系列/中外物理学精品书系
- - 作者：王大钧//王其申//(美)何北昌|责编:潘丽娜
  - 出版社：北京大学
  - ISBN：9787301314968
  - 出版日期：2020/09/01
  - 页数：395
- 售价：39.2

内容大纲
本书是一本中外物理学精品书系丛书中的物理学术专著，内容包括：弹性结构线性振动的定性性质，其中主要是模态（含固有频率和振型）的定性性质；线性弹性力学和线性结构理论的静力解、模态解和动力响应解的存在性，应用Ritz近似法求解的收敛性，以及结构理论模型的合理性等基础理论。本书可以作为有关力学及结构工程专业的研究生教材，也可作为从事力学理论研究和在结构工程、机械工程中进行振动试验、计算和设计的众多同行的参考书。
作者介绍
目录
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
1.4 Theoretical and Practical Significance of the Qualitative Theory
in Structural Mechanics
1.5 Overview of Qualitative Properties of Vibration Associated
with Bars
1.6 Overview of Qualitative Properties of Vibration Associated
with Beams
1.7 Overview of Qualitative Properties of Vibration and Static
Deformation Associated with Repetitive Structures
1.8 Overview of the Existence of Solutions in Elasticity and
Structural Theories as Well as Other Subjects in Fundamental
Theories
References
2 Oscillatory Matrices and Kernels as Well as Properties
of Eigenpairs
2.1 A Few Notations and Definitions
2.2 Some Relationships Among Minors
2.3 Jacobian Matrix
2.4 Oscillatory Matrices
2.5 Perron's Theorem and Compound Matrices
2.6 Eigenpairs of an Oscillatory Matrix
2.7 Integral Equations with Symmetric Kernels and the Concept
of Oscillatory Kernels
2.8 Perron's Theorem for Integral Equations and the Concept
of Compound Kernels
2.9 Eigenpairs of the Integral Equation with an Oscillatory
Kernel
2.10 Relationship Among Oscillatory Properties in Static
Deformation, Flexibility Functions (Matrices) Being Oscillatory
Kernels (Matrices), and Oscillatory Properties in Vibration
2.11 From Oscillatory Matrices to Oscillatory Kernels
References
3 Qualitative Properties of Vibration and Static Deformation
Associated with Discrete Systems of Strings and Bars
3.1 Discrete Systems of Strings and Bars
3.2 Basic Qualitative Properties of Vibration and Static
Deformation of Spring-Mass Systems
3.3 Necessary and Sufficient Conditions for Mode Shapes
of a Spring-Mass System
3.4 Modal Qualitative Properties of the Finite Difference System
of a Bar
3.5 Modal Qualitative Properties of the Finite Element System
of a Bar
3.6 Modal Qualitative Properties of the System Consisting of a
Massless Elastic Bar and a Number of Concentrated Masses

3.7 Modal Qualitative Properties of Discrete Systems of Strings
and Bars on Elastic Foundations
References
Qualitative Properties of Vibration and Static Deformation
Associated with Discrete Systems of Beams
4.1 The Finite Difference Model of a Beam and the Corresponding
Physical Model
4.2 Qualitative Properties of Vibration and Static Deformation
Associated with Finite Difference Systems of Well-Constrained
Beams
4.3 Modal Qualitative Properties of the Finite Difference System
of an Under-Constrained Beam
4.4 Numbers of Sign Reversals of Various Mode Shapes
Associated with the Finite Difference Systems of Beams
4.5 Construction of the Finite Difference System of a Beam
Using Modes
4.6 Interlacement of Natural Frequencies of the Finite Difference
System Modeling a Beam Subject to Various Boundary
Constraints
4.7 Oscillatory Properties of Finite Element Systems of a Beam...
4.8 Modal Qualitative Properties of Discrete Systems
of Multi-Span Beams
4.9 Modal Qualitative Properties of Discrete Systems
of Overhang Beams
References
5 Qualitative Properties of Vibration and Static Deformation
of the Sturm-Liouville System
5.1 Natural Vibration of the Sturm-Liouville System
5.2 Green's Function of the Sturm-Liouville System
5.3 Oscillatory Properties in Vibration and Static Deformation
of the Sturm-Liouville System
5.4 Number of Independent Modes of a Bar and Additional
Properties of Its Modal Shapes
5.5 Interlacement of Natural Frequencies of a Bar Subject
to Various Boundary Constraints
5.6 Comparison Between Discrete and Continuous Systems
References
6 Qualitative Properties of Vibration and Static Deformation
Associated with Continuous Systems of Beams
6.1 Differential Equation and Boundary Constraints
of a Vibrating Beam
6.2 Green's Function of a Beam
6.3 Oscillatory Properties in Static Deformation and Vibration
of a Well-Constrained Beam
6.4 Oscillatory Properties in Vibration of an Under-Constrained
Beam
6.5 Number of Independent Modes of a Beam
6.6 Additional Properties of Natural Frequencies of a Beam
6.7 Modal Qualitative Properties of the Continuous System
of an Overhang Beam

References
7 Qualitative Properties of Vibration and Static Deformation of
Repetitive Structures
7.1 Modal Qualitative Properties of Symmetric Structures
7.2 Modal Qualitative Properties of Rotationally Periodic
Structures
7.3 Modal Qualitative Properties of Linearly Periodic Structures...
7.4 Modal Qualitative Properties of Chain Structures
7.5 Modal Qualitative Properties of Axisymmetric Structures
7.6 Qualitative Properties of Forced Vibration of Repetitive
Structures
7.7 Dimension Reduction in Vibration and Shape Control
of Repetitive Structures
7.8 Qualitative Properties in Static Deformation of Repetitive
Structures
References
Theory on the Existence of Solutions in Structural Mechanics
8.1 Introduction
8.2 Variational Solutions for Three Categories of Problems in
Structural Theories
8.3 Existence of the Extremum of a Functional
8.4 Existence of Solutions of Static Deformation and Vibrational
Modes in Elasticity
8.5 Existence of Solutions of Static Deformation and Vibrational
Modes in Structural Theories
8.6 Validity of Models in Structural Theories
8.7 Convergence of the Ritz Method for Problem Solving in
Structural Theories
References
Index

内容大纲

作者介绍

目录

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