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 2100433B