| |
| |
| |
| 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 | |