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 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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