| |

| |

| |

Preliminaries | |

| |

| |

| |

Degrees of Freedom | |

| |

| |

| |

Equivalent Systems | |

| |

| |

| |

Extension/Contraction of Elastic Rods | |

| |

| |

| |

Bending of Elastic Beams | |

| |

| |

| |

Torsion of Elastic Rods | |

| |

| |

| |

Floating Bodies | |

| |

| |

| |

The Viscous Damper | |

| |

| |

| |

Aero/Hydrodynamic Damping (Drag) | |

| |

| |

| |

Springs Connected in Parallel and in Series | |

| |

| |

| |

Springs in Parallel | |

| |

| |

| |

Springs in Series | |

| |

| |

| |

A Brief Review of Complex Numbers | |

| |

| |

| |

A Review of Elementary Dynamics | |

| |

| |

| |

Kinematics of Particles | |

| |

| |

| |

Kinetics of a Single Particle | |

| |

| |

| |

Dynamics of Particle Systems | |

| |

| |

| |

Kinematics of Rigid Bodies | |

| |

| |

| |

(Planar) Kinetics of Rigid Bodies | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Free Vibration of Single Degree of Freedom Systems | |

| |

| |

| |

Free Vibration of Undamped Systems | |

| |

| |

| |

Governing Equation and System Response | |

| |

| |

| |

The Effect of Gravity | |

| |

| |

| |

Work and Energy | |

| |

| |

| |

The Simple Pendulum | |

| |

| |

| |

Free Vibration of Systems with Viscous Damping | |

| |

| |

| |

Equation of Motion and General System Response | |

| |

| |

| |

Underdamped Systems | |

| |

| |

| |

Logarithmic Decrement | |

| |

| |

| |

Overdamped Systems | |

| |

| |

| |

Critically Damped Systems | |

| |

| |

| |

Coulomb (Dry Friction) Damping | |

| |

| |

| |

Stick-Slip Condition | |

| |

| |

| |

System Response | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Forced Vibration of Single Degree of Freedom Systems &3- 1: Periodic Excitation | |

| |

| |

| |

Standard Form of the Equation of Motion | |

| |

| |

| |

Superposition | |

| |

| |

| |

Harmonic Forcing | |

| |

| |

| |

Formulation | |

| |

| |

| |

Steady State Response of Undamped Systems | |

| |

| |

| |

Steady State Response of Systems with Viscous Damping | |

| |

| |

| |

Force Transmission and Vibration Isolation | |

| |

| |

| |

Structural Damping | |

| |

| |

| |

Linear Hereditary Materials | |

| |

| |

| |

Steady State Response of Linear Hereditary Materials | |

| |

| |

| |

Steady State Response of Single Degree of Freedom Systems | |

| |

| |

| |

Selected Applications | |

| |

| |

| |

Harmonic Motion of the Support | |

| |

| |

| |

Unbalanced Motor | |

| |

| |

| |

Synchronous Whirling of Rotating Shafts | |

| |

| |

| |

Response to General Periodic Loading | |

| |

| |

| |

General Periodic Excitation | |

| |

| |

| |

Steady State Response | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Forced Vibration of Single Degree of Freedom Systems - 2: Nonperiodic Excitation | |

| |

| |

| |

Two Generalized Functions | |

| |

| |

| |

The Dirac Delta Function (Unit Impulse) | |

| |

| |

| |

The Heaviside Step Function (Unit Step) | |

| |

| |

| |

Relation Between the Unit Step and the Unit Impulse | |

| |

| |

| |

Impulse Response | |

| |

| |

| |

Impulsive and Nonimpulsive Forces | |

| |

| |

| |

Response to an Applied Impulse | |

| |

| |

| |

Response to Arbitrary Excitation | |

| |

| |

| |

Response to Step Loading | |

| |

| |

| |

Response to Ramp Loading | |

| |

| |

| |

Transient Response by Superposition | |

| |

| |

| |

The Rectangular Pulse | |

| |

| |

| |

Linear Transition to Constant Load Level | |

| |

| |

| |

Shock Spectra | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Operational Methods | |

| |

| |

| |

The Laplace Transform | |

| |

| |

| |

Laplace Transforms of Basic Functions | |

| |

| |

| |

Shifting Theorem | |

| |

| |

| |

Laplace Transforms of the Derivatives of Functions | |

| |

| |

| |

Convolution | |

| |

| |

| |

Free Vibrations | |

| |

| |

| |

Forced Vibrations | |

| |

| |

| |

The Governing Equations | |

| |

| |

| |

Steady State Response | |

| |

| |

| |

Transient Response | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Dynamics of Multi-Degree of Freedom Systems | |

| |

| |

| |

Newtonian Mechanics of Discrete Systems | |

| |

| |

| |

Mass-Spring Systems | |

| |

| |

| |

The Double Pendulum | |

| |

| |

| |

Two-Dimensional Motion of a Rigid Frame | |

| |

| |

| |

Lagrange's Equations | |

| |

| |

| |

Virtual Work | |

| |

| |

| |

The Canonical Equations | |

| |

| |

| |

Implementation | |

| |

| |

| |

The Rayleigh Dissipation Function | |

| |

| |

| |

Symmetry of the System Matrices | |

| |

| |

| |

The Stiffness Matrix | |

| |

| |

| |

The Mass Matrix | |

| |

| |

| |

The Damping Matrix | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Free Vibration of Multi-Degree of Freedom Systems | |

| |

| |

| |

The General Free Vibration Problem and Its Solution | |

| |

| |

| |

Unrestrained Systems | |

| |

| |

| |

Properties of Modal Vectors | |

| |

| |

| |

The Scalar Product | |

| |

| |

| |

Orthogonality | |

| |

| |

| |

Normalization | |

| |

| |

| |

Systems with Viscous Damping | |

| |

| |

| |

System Response | |

| |

| |

| |

State Space Representation | |

| |

| |

| |

Evaluation of Amplitudes and Phase Angles | |

| |

| |

| |

Undamped Systems | |

| |

| |

| |

Systems with General Viscous Damping | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Forced Vibration of Multi-Degree of Freedom Systems | |

| |

| |

| |

Introduction | |

| |

| |

| |

Steady State Response to Harmonic Excitation | |

| |

| |

| |

The Simple Vibration Absorber | |

| |

| |

| |

Modal Coordinates | |

| |

| |

| |

Principal Coordinates | |

| |

| |

| |

Coordinate Transformations | |

| |

| |

| |

Modal Coordinates | |

| |

| |

| |

General Motion in Terms of the Natural Modes | |

| |

| |

| |

Linear Independence of the Set of Modal Vectors | |

| |

| |

| |

Modal Expansion | |

| |

| |

| |

Decomposition of the Forced Vibration Problem | |

| |

| |

| |

Solution of Forced Vibration Problems | |

| |

| |

| |

Mode Isolation | |

| |

| |

| |

Rayleigh Damping | |

| |

| |

| |

Systems with General Viscous Damping | |

| |

| |

| |

Steady State Response to Harmonic Excitation | |

| |

| |

| |

Eigenvector Expansion | |

| |

| |

| |

Decomposition of the Forced Vibration Problem | |

| |

| |

| |

Solution of Forced Vibration Problems | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Dynamics of One-Dimensional Continua | |

| |

| |

| |

Mathematical Description of 1-D Continua | |

| |

| |

| |

Correspondence Between Discrete and Continuous Systems | |

| |

| |

| |

The Scalar Product and Orthogonality | |

| |

| |

| |

Characterization of Local Deformation | |

| |

| |

| |

Relative Extension of a Material Line Element | |

| |

| |

| |

Distortion | |

| |

| |

| |

Longitudinal Motion of Elastic Rods | |

| |

| |

| |

Torsional Motion of Elastic Rods | |

| |

| |

| |

Transverse Motion of Strings and Cables | |

| |

| |

| |

Transverse Motion of Elastic Beams | |

| |

| |

| |

Kinematical and Constitutive Relations | |

| |

| |

| |

Kinetics | |

| |

| |

| |

Euler-Bernoulli Beam Theory | |

| |

| |

| |

Rayleigh Beam Theory | |

| |

| |

| |

Timoshenko Beam Theory | |

| |

| |

| |

Geometrically Nonlinear Beam Theory | |

| |

| |

| |

Translating 1-D Continua | |

| |

| |

| |

Kinematics of a Material Particle | |

| |

| |

| |

Kinetics | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Free Vibration of One-Dimensional Continua | |

| |

| |

| |

The General Free Vibration Problem | |

| |

| |

| |

Free Vibration of Uniform Second Order Systems | |

| |

| |

| |

The General Free Vibration Problem and Its Solution | |

| |

| |

| |

Longitudinal Vibration of Elastic Rods | |

| |

| |

| |

Torsional Vibration of Elastic Rods | |

| |

| |

| |

Transverse Vibration of Strings and Cables | |

| |

| |

| |

Free Vibration of Euler-Bernoulli Beams | |

| |

| |

| |

Free Vibration of Euler-Bernoulli Beam-Columns | |

| |

| |

| |

Free Vibration of Rayleigh Beams | |

| |

| |

| |

Free Vibration of Timoshenko Beams | |

| |

| |

| |

Normalization of the Modal Functions | |

| |

| |

| |

Orthogonality of the Modal Functions | |

| |

| |

| |

Systems Whose Mass Operators Are Scalar Functions | |

| |

| |

| |

Second Order Systems | |

| |

| |

| |

Euler-Bernoulli Beams and Beam-Columns | |

| |

| |

| |

Rayleigh Beams | |

| |

| |

| |

Timoshenko Beams | |

| |

| |

| |

Evaluation of Amplitudes and Phase Angles | |

| |

| |

| |

Systems Possessing a Single Scalar Mass Operator | |

| |

| |

| |

Rayleigh Beams | |

| |

| |

| |

Timoshenko Beams | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

| |

Forced Vibration of One-Dimensional Continua | |

| |

| |

| |

Modal Expansion | |

| |

| |

| |

Linear Independence of the Modal Functions | |

| |

| |

| |

Generalized Fourier Series | |

| |

| |

| |

Decomposition of the Forced Vibration Problem | |

| |

| |

| |

Solution of Forced Vibration Problems | |

| |

| |

| |

Axially Loaded Elastic Rods | |

| |

| |

| |

Torsion of Elastic Rods | |

| |

| |

| |

Strings and Cables | |

| |

| |

| |

Euler-Bernoulli Beams | |

| |

| |

| |

Rayleigh Beams | |

| |

| |

| |

Timoshenko Beams | |

| |

| |

| |

Concluding Remarks | |

| |

| |

Bibliography | |

| |

| |

Problems | |

| |

| |

Index | |