基于切比雪夫-李茲法的結(jié)構(gòu)元三維振動分析

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