Analytical Methods in Vibrations

Analytical Methods in Vibrations
اسم المؤلف
Leonard Meirovitch
التاريخ
13 أغسطس 2019
المشاهدات
التقييم
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Analytical Methods in Vibrations
Leonard Meirovitch
Contents
Introduction Xv
Chapter 1. Behavior of Systems
1-1 Introduction
1-2 Harmonic Oscillator
1-3 Spring-mass-damper System. Free Vibration
1-4 System Response. Transfer Function
1-5 Indicial Response. Unit Step Function
1-6 * Impulsive Response. Unit Impulse
1-7 Duhamel S Integral. Convolution Integral
1-8 Response to Harmonic Excitation
1-9 Response to Periodic Excitation. Fourier Series
1-10 Response to Nonperiodic Excitation. Fourier Integral
Problems
Selected Readings
Chapter 2. Advanced Principles of Dynamics
2-1 General Considerations
2-2 Work and Energy. Single Particle
2-3 Strain Energy. Elasticity
2-4 Systems With Constraints. Degree of Freedom
2-5 Generalized Coordinates
2-6 Principle of Virtual Work. Static Case
2-7 D Alembert S Principle
2-8 Variational Principles. Hamilton S Principle
2-9 Lagrange S Equation. (Holonomic Systems)
Problems
Selected Readings
Chapter 3. Special Concepts for Vibration Study
3-1 Introduction
3-2 Influence Coefficients and Functions
3-3 Strain Energy in Terms of Influence Coefficients and
Functions. Properties of Influence Coefficients and
Functions
3-4 Lagrange S Equations of Motion in Matrix Form
3-5 Linear Transformations. Coupling
Problems
Selected Readings
Chapter 4. Natural Modes of Vibration. Discrete Systems
4-1 General Discussion
4-2 Small Oscillations of Conservative Systems. Free
Vibration
4-3 Eigenvalue Problem. Natural Modes of Vibration
4-4 Solution of the Eigenvalue Problem. Characteristic
Determinant
4-5 Orthogonality of Characteristic Vectors
4-6 Matrix Iteration Method. Sweeping Technique
4-7 Geometric Interpretation of the Eigenvalue Problem
4-8 Diagonalization by Successive Rotations Method. The
Jacobi Method
4-9 Semidefinite Systems. Unrestrained Systems
4-10 Enclosure Theorem
4-11 Rayleigh S Quotient. Properties of Rayleigh S Quotient 117
4-12 the General Eigenvalue Problem
Problems
Selected Readings
Chapter 5. Natural Modes of Vibration. Continuous Systems
5-1 General Considerations
5-2 Boundary-value Problem Formulation
5-3 the Eigenvalue Problem
5-4 General Formulation of the Eigenvalue Problem
5-5 Generalized Orthogonality. Expansion Theorem
5-6 Vibration of Strings
5-7 Longitudinal Vibration of Rods
5-8 Boundary Conditions Depending on the Eigenvalue a
5-9 Torsional Vibration of Bars
5-10 Bending Vibration of Bars
5-11 Vibration of Membranes ,
5-12 Vibration of Plates
5-13 Enclosure Theorem
5-14 Rayleigh S Quotient and Its Properties
5-15 Eigenvalue Problem. Integral Formulation
Problems
Selected Readings
Chapter 6. Natural Modes of Vibration. Approximate Methods 205
6-1 General Discussion
6-2 Rayleigh S Energy Method
6-3 Rayleigh-ritz Method
6-4 Rayleigh-ritz Method. Re-examination of the
Boundary Condition Requirements
6-5 Assumed-modes Method. Lagrange S Equations
6-6 Galerkin S Method
6-7 Collocation Method
6-8 Assumed-modes Method. Integral Formulation
6-9 Galerkin S Method. Integral Formulation
6-10 Collocation Method. Integral Formulation
6-11 Holzer S Method for Torsional Vibration
6-12 Myklestad S Method for Bending Vibration
6-13 Lumped-parameter Method Employing Influence
Coefficients
6-14 Lumped-parameter Method. Semidefinite Systems
Problems
Selected Readings
Chapter 7. Undamped System Response
7-1 General Considerations
Part a—response of Undamped Discrete
Systems 276
7-2 General Formulation. Laplace Transform Solution
7-3 Response to Initial Displacements and Velocities
7-4 Response to Harmonic Excitation
7-5 Response to Periodic Excitation. Fourier Series
7-6 Response of Discrete Systems by Modal Analysis
Part B—response of Undamped Continuous
Systems 287
7-7 General Formulation. Modal Analysis
7-8 Response of an Unrestrained Rod in Longitudinal
Motion
7-9 Response of a Simply Supported Beam to Initial
Displacements
7-10 Response of a Beam to a Traveling Force
7-11 Response of a Circular Membrane
7-12 Response of a Simply Supported Rectangular Plate
7-13 Response of a System With Moving Supports
7-14 Vibration of a System With Time-dependent Boundary
Conditions
Part C—response of Undamped Continuous
Systems. Approximate Methods 308
7-15 Assumed-modes Method. System Response
7-16 Galerkin S Method. System Response
7-17 Collocation Method. System Response
Problems
Selected Readings
Chapter 8. Transform Method Solutions of Continuous Systems. Wave
Solutions
8-1 General Considerations
8-2 the Wave Equation
8-3 Free Vibration of an Infinite String. Characteristics
8-4 Free Vibration of a Semi-infinite String
8-5 Response of a Finite String to Initial Excitation
8-6 Motion of a Bar With a Prescribed Force on One End
8-7 Wave Motion of a Bar in Bending Vibration
8-8 Free Bending Vibration of an Infinite Bar
8-9 Semi-infinite Beam With Prescribed End Motion
8-10 Bending Vibration of a Bar Hinged at Both Ends and
With a Moment Applied at One End
8-11 Free Vibration of an Infinite Membrane. Fourier Transform Solution
8-12 Hankel Transform. Relation Between Hankel and
Fourier Transforms
8-13 Response of an Infinite Membrane. Hankel Transform
Solution
8-14 Response of an Infinite Plate. Hankel Transform
Solution
8-15 Nonsymmetrical Response of an Infinite Plate. Fourier
Transform Solution
Problems
Selected Readings
Chapter 9. Damped Systems
9-1 General Discussion
9-2 Existence of Normal Modes in Viscously Damped
Discrete Systems
9-3 Forced Vibration of Viscously Damped Systems. Modal
Analysis
9-4 the Concept of Structural Damping
9-5 Structurally Damped Discrete Systems
9-6 General Case of Viscously Damped Discrete Systems.
Laplace Transform Solution
9-7 General Case of Damping. Introduction to Modal
Analysis
9-8 Solution of the Eigenvalue Problem. Characteristic
Determinant
9-9 Orthogonality of Modes
9-10 Solution of the Eigenvalue Problem. Matrix Iteration
Method
9-11 Forced Vibration of Viscously Damped Discrete Systems.
General Case
9-12 Damped Continuous Systems. Viscous Damping
9-13 Damped Continuous Systems. Structural Damping
Problems
Selected Readings
Chapter 10. Vibration Under Combined Effects
10-1 Introduction
10-2 Transverse Vibration of a Bar on an Elastic Foundation 437
10-3 Effect of Axial Forces on the Bending Vibration of a
Bar. General Equations
10-4 Vibration of Rotating Bars
10-5 Effect of a Constant Axial Force on the Transverse
Vibration of a Uniform Free-free Bar
10-6 Natural Modes of Bars Under Combined Flexure and
Torsion
10-7 Effect of Axial Forces on the Natural Modes of
Vibration of a Nonuniform Free-free Bar
Problems
Selected Readings
Chapter 11. Random Vibration
11-1 Introduction
11-2 Probability
11-3 Random Variables and Probability Distributions
11-4 Ensemble Averages. Stationary Random Processes
11-5 Time Averages. Ergodic Random Processes
11-6 Normal Random Process. Central Limit Theorem
11-7 Spectral Density of a Stationary Random Process
11-8 Correlation Theorem. Parseval S Theorem
11-9 Spectral Densities of Sample Functions. Ergodic
Processes
11-10 Response of Linear Systems to Stationary Random
Excitation. General Relations
11-11 Response of Linear Systems to Ergodic Excitation.
General Relations
11-12 Response of a Single-degree-of-freedom System to
Random Excitation
11-13 Response of a Discrete System to Random Excitation
Response of Continuous Systems to Random Excitation 508
Problems
Selected Readings
Appendix a. Elements of Matrix Algebra
General Considerations
Principal Types of Matrices and Their Notation
Basic Matrix Operations
Determinant of a Square Matrix. Singular Matrix
Adjoint of a Matrix
Inverse, or Reciprocal, of a Matrix
Transposition and Reciprocation of Products of
Matrices
Linear Transformations
Selected Readings
Appendix B. Elements of Laplace Transformation 527
Integral Transformations. General Discussion
The Laplace Transformation. Definition
First Shifting Theorem (in the Complex Plane)
Transformation of Derivatives
Transformation of Ordinary Differential Equations
The Inverse Transformation
Method of Partial Fractions
Second Shifting Theorem (in the Real Domain)
The Convolution Integral. Borel S Theorem
Selected Readings
Appendix C. Elements of Fourier Transformation 536
General Definitions
Fourier Integral Formula
Inversion Formulas
Fourier Transforms of Derivatives of Functions
Finite Fourier Transforms
Finite Fourier Transforms of Derivatives of Functions
Convolution Theorems
Selected Readings
Index 545
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