Vibrations, Dynamics and Structural Systems

Cover
Half Title
Title Page
Copyright Page
Dedication
Preface to Second Edition
Preface to First Edition
Table of Contents
Chapter 1: Introduction
1.1 Introduction
1.2 Brief History of Vibrations
1.3 Comparison Between Static and Dynamic Analysis
1.4 D’Alembert’s Principle
1.5 Some Basic Definitions
1.6 Dynamic Loading
1.7 Finite Element Discretization
1.8 Response of the System
1.9 Types of Analysis
1.10 Linear and Nonlinear Vibration
References
Chapter 2: Free Vibration of Single Degree of Freedom System
2.1 Introduction
2.2 Equation of Motion of Single Degree of Freedom (SDF) System
2.3 Free Undamped Vibration of the SDF System
2.4 Free Damped Vibration of SDF System
2.5 Free Vibration with Coulomb Damping
2.6 Energy Method and Free Torsional Vibration
2.7 Logarithmic Decrement
References
Exercise 2
Chapter 3: Forced Vibration of Single Degree of Freedom System
3.1 Introduction
3.2 Response of Damped Systems to Harmonic Loading
3.3 Rotating Unbalance
3.4 Reciprocating Unbalance
3.5 Whirling of Rotating Shafts
3.6 Vibration Isolation and Transmissibility
3.7 Energy Dissipation by Damping
3.8 Equivalent Viscous Damping
3.9 Self-Excited Vibrations
3.10 Vibration Measuring Seismic Instruments
3.11 Response of Structures Due to Transient Vibration
3.12 Response of the SDF System to a General Type of Forcing Function
3.13 Dynamic Load Factor and Response Spectrum
3.14 Response Due to Periodic Forces
3.15 Response Due to Nonperiodic Excitation
3.16 Relationship Between Complex Frequency Response Function and Unit Impluse Response Function
3.17 Support Motion
3.18 Response of SDF Systems Related to Earthquakes
3.19 Techniques for Analysing Earthquake Response
References
Exercise 3
Chapter 4: Numerical Methods in Structural Analysis: Applied to SDF Systems
4.1 Introduction
4.2 Direct Integral Techniques
4.3 Numerical Evaluation of Duhamel’s Integral
4.4 Numerical Computation in Frequency Domain
References
Exercise 4
Chapter 5: Vibration of Two Degrees of Freedom System
5.1 Introduction
5.2 Free Vibration of Undamped Two Degrees of Freedom Systems
5.3 Torsional Vibration of Two Degrees of Freedom System
5.4 Forced Vibration of Two Degrees of Freedom Undamped System
5.5 Vibration Absorber
5.6 Free Vibration of Two Degrees of Freedom System with Viscous Damping
5.7 Coordinate Coupling
5.8 Free Vibration of Damped Two Degrees of Freedom System
References
Exercise 5
Chapter 6: Free Vibration of Multiple Degrees of Freedom System
6.1 Introduction
6.2 Equations of Motion of MDF Systems
6.3 Free Undamped Vibration Analysis of MDF Systems
6.4 Orthogonality Relationship
6.5 Eigenvalue Problem
6.6 Determination of Absolute Displacement of Free Vibration of MDF Systems
6.7 Eigenvalue Solution Techniques
6.8 Dunkerley’s Equation
6.9 Holzer Method
6.10 Transfer Matrix Method
6.11 Myklestad Method
6.12 Stodola’s Method
6.13 Matrix Deflation Procedure
6.14 Rayleigh’s Method
6.15 Rayleigh-Ritz Method
6.16 Subspace Iteration Method
6.17 Simultaneous Iteration Method and Algorithm
6.18 Geared Systems
6.19 Branched Systems
6.20 Reduction Methods for Dynamic Analysis
6.21 Component Mode Synthesis Method
6.22 Lagrange’s Equation
References
Exercise 6
Chapter 7: Forced Vibration Analysis of Multiple Degrees of Freedom System
7.1 Introduction
7.2 Mode Superposition Method for the Determination of Response of MDF System
7.3 Mode Acceleration Method for the Determination of Response of MDF System
7.4 Response of MDF Systems Under the Action of Transient Forces
7.5 Damping in MDF Systems
7.6 Response of MDF Systems to Support Motion
7.7 Earthquake Spectrum Analysis of Structures Having MDF Systems
7.8 Use of Response Spectra for Designing MDF Systems
7.9 Direct Integration for Determining Response of MDF Systems
7.10 Complex Matrix Inversion Method for Forced Vibration Analysis of MDF Systems
7.11 Frequency Domain Analysis of MDF Systems by Modal Superposition for Harmonic Loads
7.12 Frequency Domain Analysis of Direct Frequency Response Method
References
Exercise 7
Chapter 8: Free Vibration Analysis of Continuous Systems
8.1 Introduction
8.2 Vibration of Strings
8.3 Free Longitudinal Vibration of a Bar
8.4 Free Torsional Vibration of the Shaft
8.5 Free Flexural Vibration of Beams
8.6 Free Flexural Vibration of Simply Supported Beam
8.7 Free Flexural Vibration of Beams with Other End Conditions
8.8 Free Flexural Vibration of Beams with General End Conditions
8.9 Orthogonality Properties of Normal Modes
8.10 Effect of Rotary Inertia on the Free FLexural Vibration of Beams
8.11 Free Vibration of the Shear Beam
8.12 Effect of Axial Force on the Free Flexural Vibration of Beams
8.13 Free Vibration of Beams Including Shear Deformation and Rotary Inertia Effects
8.14 Collocation Method for Obtaining Normal Modes of Vibration of a Continuous Systems
8.15 Rayleigh’s Quotient for Fundamental Frequency
8.16 Rayleigh-Ritz Method for Determining Natural Frequencies for Continuous Systems
8.17 Vibration of Membranes
8.18 Transverse Vibration of Rectangular Thin Plates
References
Exercise 8
Chapter 9: Forced Vibration of Continuous Systems
9.1 Introduction
9.2 Forced Axial Vibration of Bars
9.3 Forced Vibration of the Shear Beam Under Ground Motion Excitation
9.4 Forced Vibration of Flexural Member
9.5 Forced Transverse Vibration of Uniform Damped Beam
9.6 Forced Vibration of Flexural Member Subjected to Ground Motion Excitation
9.7 Response of Beams Due to Moving Loads
References
Exercise 9
Chapter 10: Dynamic Direct Stiffness Method
10.1 Introduction
10.2 Continuous Beam
10.3 Method Analogous to Classical Methods in Statical Analysis
10.4 Dynamic Stiffness Matrix in Bending
10.5 Dynamic Stiffness Matrix for Flexural and Rigid Axial Displacements
10.6 Dynamic Stiffness Matrix of a Bar Undergoing Axial Deformation
10.7 Dynamic Stiffness Matrix of a Bar Subjected to Axial and Bending Deformation
10.8 Beam Segments with Distributed Mass Having Shear Deformation and Rotary Inertia
References
Exercise 10
Chapter 11: Vibration of Ship and Aircraft as A Beam
11.1 Introduction
11.2 Shift in Stiffness Matrix
11.3 Added Mass of a Ship
11.4 Flexibility Matrix Method for Determining Natural Frequencies of a Free-Free Beam in Vertical Vibration
11.5 Flexibility Matrix Method for the Analysis of Coupled Horizontal and Torsional Vibration
11.6 Numerical Examples
References
Exercise 11
Chapter 12: Finite Element Method in Vibration Analysis
12.1 Introduction to the Finite Element Method
12.2 Torsional Vibration of Shafts
12.3 Axial Vibration of Rods
12.4 Flexural Vibration of Beams
12.5 Vibration of Timoshenko Beams
12.6 lnplane Vibration of Plates
12.7 Flexural Vibration of Plates
12.8 Flexural Vibrations of Plates Using Isoparametric Elements
12.9 Periodic Structures
References
Exercise 12
Chapter 13: Finite Difference Method for the Vibration Analysis of Beams and Plates
13.1 Introduction to the Finite Difference Method
13.2 Central Difference Method
13.3 Free Vibration of Beams
13.4 Free Vibration of Rectangular Plates
13.5 Semianalytic Finite Difference Method for Free Vibration Analysis of Rectangular Plates
13.6 Semianalytic Finite Difference Method for Forced Vibration Analysis of Plates
13.7 Spline Finite Strip Method of Analysis of Plate Vibration
References
Exercise 13
Chapter 14: Nonlinear Vibration
14.1 Introduction
14.2 Perturbation Method
14.3 Step-by-Step Integration
References
Chapter 15: Random Vibrations
15.1 Introduction
15.2 Random Process
15.3 Probability Distributions
15.4 Ensemble Averages, Mean and Autocorrelation
15.5 Stationary Process, Ergodic Process and Temporal Averages
15.6 Power Spectral Density
15.7 Relationship Between Autocorrelation Function and Power Spectral Density
15.8 Random Response of SDF Systems
15.9 Random Response of MDF Systems
15.10 Response of Flexural Beams Under Random Loading
15.11 Finite Element Random Response of Plates
References
Exercise 15
Chapter 16: Computer Programme in Vibration Analysis
16.1 Introduction
16.2 Computer Programme for Forced Vibration Analysis
16.3 Computer Programme for Random Vibration Analysis
16.4 Computer Programme for Free Vibration Analysis of Framed Structures
16.5 Computer Programme for Free Vibration Analysis of Ships by Flexibility Matrix Method
16.6 Computer Programme for the Free Vibration Analysis of Plates
References
Appendix A: The Stiffness Matrix
A.1 Stiffness Matrix
A.2 Direct Stiffness Method
Appendix B: Table for Spring Stiffness
Index