本书以李兹法为基础。研究结构部件的三维弹性振动特性。将试函数定义为边界特征函数与切比雪夫多项式级数的积，对于简单边界条件，直接建立边界特征函数，而对于复杂边界条件，则采用日函数方法建立边界特征函数。

本书具有内容新颖，层次分明、机理阐述深入浅出，研究结果可直接应用于工程实际的特点。在结构动力学理论和数值计算方法研究领域，是很有价值的读物。

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，第一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