Applications of Static Beam Functions in Vibration Analysis of Structures

静力梁函数在结构振动分析中的应用

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Author: Zhou Ding
Language: English
ISBN/ISSN: 9787030377876
Published on: 2013-06
Soft Cover

Applications of Static Beam Functions in Vibration Analysis of Structures
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。



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 RayleighoRitz 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 Kirchhon 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 ConclusionsChapter 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  



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