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Preliminaries | |
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Degrees of Freedom | |
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Equivalent Systems | |
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Extension/Contraction of Elastic Rods | |
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Bending of Elastic Beams | |
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Torsion of Elastic Rods | |
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Floating Bodies | |
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The Viscous Damper | |
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Aero/Hydrodynamic Damping (Drag) | |
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Springs Connected in Parallel and in Series | |
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Springs in Parallel | |
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Springs in Series | |
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A Brief Review of Complex Numbers | |
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A Review of Elementary Dynamics | |
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Kinematics of Particles | |
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Kinetics of a Single Particle | |
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Dynamics of Particle Systems | |
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Kinematics of Rigid Bodies | |
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(Planar) Kinetics of Rigid Bodies | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Free Vibration of Single Degree of Freedom Systems | |
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Free Vibration of Undamped Systems | |
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Governing Equation and System Response | |
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The Effect of Gravity | |
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Work and Energy | |
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The Simple Pendulum | |
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Free Vibration of Systems with Viscous Damping | |
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Equation of Motion and General System Response | |
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Underdamped Systems | |
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Logarithmic Decrement | |
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Overdamped Systems | |
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Critically Damped Systems | |
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Coulomb (Dry Friction) Damping | |
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Stick-Slip Condition | |
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System Response | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Forced Vibration of Single Degree of Freedom Systems &3- 1: Periodic Excitation | |
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Standard Form of the Equation of Motion | |
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Superposition | |
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Harmonic Forcing | |
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Formulation | |
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Steady State Response of Undamped Systems | |
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Steady State Response of Systems with Viscous Damping | |
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Force Transmission and Vibration Isolation | |
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Structural Damping | |
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Linear Hereditary Materials | |
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Steady State Response of Linear Hereditary Materials | |
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Steady State Response of Single Degree of Freedom Systems | |
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Selected Applications | |
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Harmonic Motion of the Support | |
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Unbalanced Motor | |
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Synchronous Whirling of Rotating Shafts | |
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Response to General Periodic Loading | |
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General Periodic Excitation | |
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Steady State Response | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Forced Vibration of Single Degree of Freedom Systems - 2: Nonperiodic Excitation | |
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Two Generalized Functions | |
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The Dirac Delta Function (Unit Impulse) | |
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The Heaviside Step Function (Unit Step) | |
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Relation Between the Unit Step and the Unit Impulse | |
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Impulse Response | |
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Impulsive and Nonimpulsive Forces | |
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Response to an Applied Impulse | |
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Response to Arbitrary Excitation | |
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Response to Step Loading | |
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Response to Ramp Loading | |
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Transient Response by Superposition | |
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The Rectangular Pulse | |
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Linear Transition to Constant Load Level | |
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Shock Spectra | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Operational Methods | |
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The Laplace Transform | |
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Laplace Transforms of Basic Functions | |
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Shifting Theorem | |
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Laplace Transforms of the Derivatives of Functions | |
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Convolution | |
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Free Vibrations | |
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Forced Vibrations | |
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The Governing Equations | |
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Steady State Response | |
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Transient Response | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Dynamics of Multi-Degree of Freedom Systems | |
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Newtonian Mechanics of Discrete Systems | |
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Mass-Spring Systems | |
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The Double Pendulum | |
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Two-Dimensional Motion of a Rigid Frame | |
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Lagrange's Equations | |
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Virtual Work | |
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The Canonical Equations | |
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Implementation | |
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The Rayleigh Dissipation Function | |
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Symmetry of the System Matrices | |
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The Stiffness Matrix | |
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The Mass Matrix | |
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The Damping Matrix | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Free Vibration of Multi-Degree of Freedom Systems | |
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The General Free Vibration Problem and Its Solution | |
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Unrestrained Systems | |
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Properties of Modal Vectors | |
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The Scalar Product | |
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Orthogonality | |
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Normalization | |
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Systems with Viscous Damping | |
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System Response | |
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State Space Representation | |
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Evaluation of Amplitudes and Phase Angles | |
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Undamped Systems | |
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Systems with General Viscous Damping | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Forced Vibration of Multi-Degree of Freedom Systems | |
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Introduction | |
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Steady State Response to Harmonic Excitation | |
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The Simple Vibration Absorber | |
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Modal Coordinates | |
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Principal Coordinates | |
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Coordinate Transformations | |
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Modal Coordinates | |
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General Motion in Terms of the Natural Modes | |
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Linear Independence of the Set of Modal Vectors | |
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Modal Expansion | |
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Decomposition of the Forced Vibration Problem | |
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Solution of Forced Vibration Problems | |
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Mode Isolation | |
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Rayleigh Damping | |
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Systems with General Viscous Damping | |
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Steady State Response to Harmonic Excitation | |
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Eigenvector Expansion | |
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Decomposition of the Forced Vibration Problem | |
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Solution of Forced Vibration Problems | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Dynamics of One-Dimensional Continua | |
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Mathematical Description of 1-D Continua | |
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Correspondence Between Discrete and Continuous Systems | |
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The Scalar Product and Orthogonality | |
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Characterization of Local Deformation | |
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Relative Extension of a Material Line Element | |
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Distortion | |
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Longitudinal Motion of Elastic Rods | |
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Torsional Motion of Elastic Rods | |
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Transverse Motion of Strings and Cables | |
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Transverse Motion of Elastic Beams | |
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Kinematical and Constitutive Relations | |
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Kinetics | |
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Euler-Bernoulli Beam Theory | |
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Rayleigh Beam Theory | |
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Timoshenko Beam Theory | |
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Geometrically Nonlinear Beam Theory | |
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Translating 1-D Continua | |
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Kinematics of a Material Particle | |
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Kinetics | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Free Vibration of One-Dimensional Continua | |
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The General Free Vibration Problem | |
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Free Vibration of Uniform Second Order Systems | |
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The General Free Vibration Problem and Its Solution | |
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Longitudinal Vibration of Elastic Rods | |
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Torsional Vibration of Elastic Rods | |
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Transverse Vibration of Strings and Cables | |
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Free Vibration of Euler-Bernoulli Beams | |
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Free Vibration of Euler-Bernoulli Beam-Columns | |
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Free Vibration of Rayleigh Beams | |
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Free Vibration of Timoshenko Beams | |
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Normalization of the Modal Functions | |
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Orthogonality of the Modal Functions | |
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Systems Whose Mass Operators Are Scalar Functions | |
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Second Order Systems | |
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Euler-Bernoulli Beams and Beam-Columns | |
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Rayleigh Beams | |
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Timoshenko Beams | |
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Evaluation of Amplitudes and Phase Angles | |
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Systems Possessing a Single Scalar Mass Operator | |
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Rayleigh Beams | |
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Timoshenko Beams | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Forced Vibration of One-Dimensional Continua | |
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Modal Expansion | |
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Linear Independence of the Modal Functions | |
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Generalized Fourier Series | |
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Decomposition of the Forced Vibration Problem | |
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Solution of Forced Vibration Problems | |
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Axially Loaded Elastic Rods | |
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Torsion of Elastic Rods | |
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Strings and Cables | |
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Euler-Bernoulli Beams | |
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Rayleigh Beams | |
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Timoshenko Beams | |
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Concluding Remarks | |
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Bibliography | |
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Problems | |
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Index | |