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  静力梁函数在结构...
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  基于切比雪夫－李...
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　　本书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-伯努利梁和铁摩辛柯梁的振动特性；第7章至第11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。 　　本书可供航空航天、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。

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• 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 Functions 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 Functions
  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 Functions
  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