周叮编著的《静力梁函数在结构振动分析中的应用》以著名的结构力学分析方法——李兹法为基础，创造性地提出了以静力梁函数作为基函数，研究梁、板结构的动力学特性，重点分析变截面和变厚度、内部支撑以及边界条件对梁、板结构振动特性的影响。可供航空航天、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。

周叮编著的《静力梁函数在结构振动分析中的应用》以著名的结构力学分析方法——李兹法为基础，创造性地提出了以静力梁函数作为基函数，研究梁、板结构的动力学特性，重点分析变截面和变厚度、内部支撑以及边界条件对梁、板结构振动特性的影响。全书共23章，第1章介绍李兹法的发展史与存在的问题；第2章至第6章研究各种边界和内部支撑条件下变截面欧拉一伯努利梁和铁摩辛柯梁的振动特性；第7章至第ll章研究各种边界和线支条件下等厚度基尔霍夫薄板的振动特性；第12章至第14章研究线支和点支等厚度复合材料薄板的振动特性；第15章和第16章研究变厚度基尔霍夫薄板的振动特性；第17章至第20章研究等厚度和变厚度米德林中厚板的振动特性：第21章和第22章研究线支和点支等厚度复合材料厚板的振动特性；第23章研究矩形储液罐的流-固耦合振动特性。

《静力梁函数在结构振动分析中的应用》可供航空航天、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

Chapter 2 Vibration Analysis of Tapered Euler-Bernoulli Beams

 2.1 Introduction

 2.2 The Rayleigh-Ritz Method for the Tapered Beams

 2.3 A New Set of Admissible Functions

2.3.1 The coefficients for a truncated beam

2.3.2 The coefficients for a sharply ended beam

2.3.3 The tapered beam with rigid body motion

 2.4 Convergency and Comparison Studies

 2.4.1 Convergency study

 2.4.2 Optimum expanding point of Taylor series

 2.5 Numerical Results

 2.6 Concluding Remarks

Chapter 3 Vibration Analysis of Tapered Euler-Bernoulli Beams with Intermediate Supports

 3.1 Introduction

 3.2 The Rayleigh-Ritz Method for Tapered Beams with Intermediate Supports

 3.3 A Set of Static Tapered Beam Functions

3.3.1 The truncated beam

3.3.2 The sharply ended beam

3.3.3 The tapered beam with motions of rigid body

 3.4 Numerical Examples

 3.5 Concluding Remarks

Chapter 4 Vibration Analysis of Multi-span Timoshenke Beams..

 4.1 Introduction

 4.2 Eigenfrequency Equation

 4.3 Static Timoshenko Beam Functions

 4.4 Convergence and Comparison Studies

 4.5 Numerical Examples

 4.6 Concluding Remarks

Chapter 5 Vibration Analysis of Tapered Timoshenke Beams

 5.1 Introduction

 5.2 Eigenfrequency Equation of Tapered Beam

 5.3 The Static Timoshenko Beam Functions （STBF）

5.3.1 Truncated beam

5.3.2 Sharply ended beam

 5.4 Convergence and Comparison Study

 5.5 Numerical Results

 5.6 Conclusions

Chapter 6 Estimation of Dynamic Characteristics of a Spring-Mass-Beam System

 6.1 Introduction

 6.2 Governing Differential Equations

 6.3 Galerkin Solutions

 6.4 Basic Characteristics of Solutions

 6.5 Static Beam Functions

 6.6 Determination of Factors

 6.7 An Example

 6.8 Characteristics of Solutions

 6.9 Conclusions

Chapter 7 Vibration Analysis of Kirchhoff Rectangular Plates

 Part I Using Static Beam Functions under Point Loads

 7.1 Introduction

 7.2 Sets of Static Beam Fhnctions under Point Loads

 7.3 Rayleigh-Ritz Solution for Rectangular Plates

 7.4 Numerical Results

 7.5 Concluding Remarks

 Part II Using Static Beam Functions under Sinusoidal Loads

 7.1 Introduction

 7.2 The Set of Static Beam Functions

 7.3 The Rayleigh-Ritz Approach

 7.4 Numerical Results

 7.5 Concluding Remarks

Chapter 8 Vibration Analysis of Kirchhoff Rectangular Plates with Elastic Edge Constraints

 8.1 Introduction

 8.2 The Set of Static Beam Functions

 8.3 The Rayleigh-Ritz Solution

 8.4 Numerical Examples

 8.5 Discussion and Conclusions

Chapter 9 Vibration Analysis of Kirchhoff Rectangular Plates with Intermediate Line-supports

 Part I Using a Combination of Vibrating Beam Functions and Polynomials

 9.1 Introduction

 9.2 Mathematical Model

 9.3 Numerical Examples

 9.4 Concluding Remarks

 Part II Using the Static Beam Functions for Beam with Point-supports.

 9.1 Introduction

 9.2 A New Set of Admissible Functions

 9.3 Eigenfrequency Equation

 9.4 Some Numerical Results

 9.5 Conclusions

Chapter 10 Vibration Analysis of Kirchhoff Rectangular Plates with Elastic Intermediate Line-supports and Edge Constraints

 10.1 Introduction

 10.2 A Set of Static Beam Fhnctions

 10.3 Formulation of Eigenvalue Equation

 10.4 Numerical Examples

 10.5 Conclusions

Chapter 11 Vibration Analysis of Kirchhoff Rectangular Plates with Elastic Point-supports

 11.1 Introduction

 11.2 Sets of Static Beam Functions under Point Loads

 11.3 Eigenvalue Problem with Rayleigh-Ritz Method

 11.4 Numerical Results

 11.5 Conclusion

Chapter 12 Vibration Analysis of Symmetrically Laminated Rectangular Plates with Intermediate Line-supports

 12.1 Introduction

 12.2 A Set of Static Beam Functions

 12.3 Eigenfrequency Equation

 12.4 Numerical Results

12.4.1 Accuracy and convergency study

12.4.2 Numerical examples

 12.5 Concluding remarks

Chapter 13 Vibration Analysis of Asymmetrically Laminated Rectangular Plates with Internal Line-supports

 13.1 Introduction

 13.2 Energy Functional

 13.3 Rayleigh-Ritz Solution

 13.4 Trial Functions

 13.5 Convergence and Comparison Study

 13.6 Numerical Results

 13.7 Conclusion

Chapter 14 Vibration Analysis of Composite Rectangular Plates with Point-supports

 14.1 Introduction

 14.2 Static Beam Functions

14.2.1 The static beam functions under sine series loads

14.2.2 The static beam functions under a point-load

 14.3 Eigenfrequency Equation

 14.4 Admissible Fhnctions

 14.5 Comparison and Convergence

14.5.1 Isotropic square plates with point-supports

14.5.2 Laminated square composite plates

 14.6 Numerical Results

 14.7 Conclusions

Chapter 15 Vibration Analysis of Tapered Kirchhoff Rectangular Plates

 15.1 Introduction

 15.2 The development of a set of tapered beam functions

 15.3 The Rayleigh-Ritz method

 15.4 Numerical examples

 15.5 Concluding remarks

 Appendix

Chapter 16 Vibration Analysis of Tapered Kirchhoff Rectangular Plates with Intermediate Line-supports

 16.1 Introduction

 16.2 The Rayleigh-Ritz Method for Tapered Rectangular Plates

 16.3 A Set of Static Beam Functions

16.3.1 The truncated beam

16,3.2 The sharp ended beam

16.3.3 The tapered beam with rigid body motions

 16.4 Numerical Examples

 16.5 Conclusions

Chapter 17 Vibration Analysis of Mindlin Rectangular Plates .-

 17.1 Introduction

 17.2 A Set of Static Timoshenko Beam Functions

 17.3 Eigenfrequency Equation of Mindlin Plate

 17.4 Comparison and Convergency Studies

 17.5 The Parametric Study

 17.6 Conclusions

Chapter 18 Vibration Analysis of Mindlin Rectangular Plates with Elastically Restrained Edges

 18.1 Introduction

 18.2 Rayleigh-Ritz Formulae for Mindlin Rectangular Plates

 18.3 A Set of Static Timoshenko Beam Functions

 18.4 Comparison and Convergency Studies

 18.5 Numerical Results

 18.6 Conclusions

Chapter 19 Vibration Analysis of Mindlin Rectangular Plates with Intermediate Line-supports

 19.1 Introduction

 19.2 Rayleigh-Ritz Solution of Mindlin Plate

 19.3 Static Timoshenko Beam Functions

 19.4 Convergence and Comparison Study

 19.5 Numerical Results

 19.6 Conclusions

Chapter 20 Vibrations Analysis of Tapered Mindlin Plates

 20.1 Introduction

 20.2 The Eigenfrequency Equation of Tapered Plates

 20.3 Two Sets of Static Timoshenko Beam Functions （STBF）

20.3.1 Truncated beam

20.3.2 Sharp-ended beam

 20.4 Convergence and Comparison Studies

 20.5 Numerical Results

 20.6 Concluding Remarks

Chapter 21 Vibration Analysis of Thick Rectangular Plates with Internal Line-supports

 21.1 Introduction

 21.2 Trial Functions

 21.3 Numerical Examples

21.3.1 Preliminary assessment: simply supported laminated plates

21.3.2 Continuous rectangular plates

 21.4 Conclusions

Chapter 22 Vibration Analysis of Layered Thick Rectangular Plates with Internal Point-supports

 22.1 Introduction

 22.2 Two Sets of Static Beam Functions

22.2.1 Static beam functions under a series of sinusoidal loads

22.2.2 Static beam functions under a series of point-loads

 22.3 Finite Layer Formulation

 22.4 Basic Functions

 22.5 Numerical Studies

22.5.1 Convergence and comparison

22.5.2 Numerical examples

 22.6 Concluding Remarks

 Appendix A

 Appendix B

Chapter 23 Vibration Analysis of Rectangular Tanks Partially Filled with Liquid

 23.1 Introduction

 23.2 Basic Equations

 23.3 Solution of Velocity Potential

 23.4 Rayleigh-Ritz-Galerkin Method

23.4.1 Rayleigh quotient

23.4.2 Eigenfrequency equation

 23.5 Admissible Functions

 23.6 Numerical Results

23.6.1 Convergence and comparison study

23.6.2 Parametric effect study

 23.7 Conclusions

References