本书以李兹法为基础，研究结构部件的三维弹性振动特性。全书共十六章，**章介绍了李兹法的历史发展和问题的由来；第二章介绍了切比雪夫多项式的定义和特点：第三章是本书的主要创新内容，建立了试函数的一般构造形式——边界特征函数与切比雪夫多项式级数的积，给出了各种边界条件下边界特征函数的具体表达方法；第四章至第十六章介绍了切比雪夫一李兹法的应用，分别研究了十三种典型结构的三维弹性动力学特性。
本书可供航天航空、机械、土木和力学等方面的科研工作者、工程设计人员、大专院校有关专业教师和研究生使用。

Preface
Chapter 1 Introduction
1.1 General Introduction
1.2 One-dimensional Vibration
1.3 Two-dimensional Vibration
1.4 Three-dimensional Vibration
Chapter 2 Chebyshev Polynomials
2.1 Introduction
2.2 Definition
2.3 Basic Properties
2.4 Some Advantages
Chapter 3 Ritz Method
3.1 Introduction
3.2 Basic Formulation
3.3 Construction of Solutions
3.4 Construction of Boundary Characteristic Functions
Chapter 4 3-D Vibration of Rectangular Plates
4.1 Introduction
4.2 Mathematical Formulation
4.3 Convergence Study and Comparison
4.4 Numerical Results
4.5 Conclusions
Chapter 5 3-D Vibration of Rectangular Plates on Pasternak Foundation
5.1 Introduction
5.2 Formulation
5.3 Convergency and Comparison
5.4 Numerical Results
5.5 Conclusions
Chapter 6 3-D Vibration of Circular and Annular Plates
6.1 Introduction
6.2 Theoretical Formulation
6.3 Convergence and Comparison Study
6.4 Numerical Results
6.5 Conclusions
Chapter 7 3-D Vibration of Circular Plates on Pasternak Foundation
7.1 Introduction
7.2 Formulation
7.3 Convergence and Comparison Study
7.4 Parametric Study
7.5 Conclusions
Chapter 8 3-D Vibration of Solid and Hollow Circular Cylinders
8.1 Introduction
8.2 Formulation
8.3 Convergence and Comparison Studies
8.4 Numerical Results
8.5 Concluding Remarks
Chapter 9 3-D Vibration of A Torus with Circular Cross-Section
9.1 Introduction
9.2 Theoretical Formulation
9.3 Convergence Study
9.4 Eigenfrequencies and Mode Shapes
9.5 Conclusions
Chapter 10 3-D Vibration of Isosceles Triangular Plates
10.1 Introduction
10.2 Theoretical Formulation
10.3 Convergence and Comparison Studies
10.4 Numerical Results
10.5 Concluding Remarks
Chapter 11 3-D Vibration of Prisms with Isosceles Triangular Cross-sections
11.1 Introduction
11.2 Formulation
11.3 Convergence and Comparison Study
11.4 Numerical Results
11.5 Conclusion
Chapter 12 3-D Vibration of Skew Thick Plates
12.1 Introduction
12.2 Theoretical Formulation
12.3 Convergence and Comparison Studies
12.4 Numerical Results
12.5 Conclusions
Chapter 13 3-D Vibration of Prisms with Skew Cross-section
13.1 Introduction
13.2 Mathematical Formulation
13.3 Convergence and Results
13.4 Conclusions
Chapter 14 3-D Vibration of Generalized Super Elliptical Plates
14.1 Introduction
14.2 Formulation
14.3 Convergence and Comparison Study
14.4 Parametric Study
14.5 Concluding Remark
Chapter 15 3-D Vibration of Thick Circular Plates with Built-in Edges.
15.1 Introduction
15.2 Theoretical Formulation
15.3 Convergence and Comparison Studies
15.4 Parametric Studies
15.5 Conclusions
Chapter 16 3-D Vibration of Rectangular Plates with Mixed Boundary Conditions
16.1 Introduction
16.2 Model
16.3 Basic Formulae
16.4 Boundary Characteristic Functions
16.5 Convergence Study
16.6 Comparison Study
16.7 Numerical Results
16.8 Conclusions
References