静力梁函数在结构振动分析中应用

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 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

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

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

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

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

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

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

Chapter 15 Vibration Analysis of Tapered Kirchhoff Rectangular Plates

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

Chapter 17 Vibration Analysis of Mindlin Rectangular Plates

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

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

Chapter 20 Vibrations Analysis of Tapered Mindlin Plates

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

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

Chapter 23 Vibration Analysis of Rectangular Tanks Partially Filled with Liquid

References

《结构工程前沿丛书：静力梁函数在结构振动分析中的应用（英文版）》针对经典的欧拉梁理论和克西霍夫理论，以及铁木辛柯梁理论和米德林中厚板理论，分别建立个了各自的静力梁函数。取这些静力梁函数作为试函数，利用李兹法导出特征方程。研究结果表明，静力梁函数法不但能够给出高精度的固有频率，而且能够给出高精度的动力响应，特别是能够很好地模拟内部线支引起的剪力跳跃。《结构工程前沿丛书：静力梁函数在结构振动分析中的应用（英文版）》共21个章节，从变厚度欧拉梁的动力学特性计算直到储液罐的流-固耦合振动分析结束。内容构成一个完整的应用体系。《结构工程前沿丛书：静力梁函数在结构振动分析中的应用（英文版）》的研究方法，系作者首次独立提出，其中的绝大部分内容，均已被作者发表于国际著名的核心期刊