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| Equations of Motion for Discrete Systems | |
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| The Study of Vibrations: An Overview | |
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| System Elements | |
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| Generalized Coordinates | |
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| Newton-Euler Motion Equations | |
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| Power Balance Method for Time-Invariant Systems | |
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| Power Balance Law | |
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| Linearized Energy and Power | |
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| Linearized Equations of Motion | |
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| Implementation | |
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| References and Selected Readings | |
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| Exercises | |
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| Transient Response of One-Degree-of-Freedom System | |
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| Harmonic Functions | |
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| Basic Properties | |
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| Complex Variable Representation | |
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| Algebraic Operations | |
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| Free Vibration | |
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| Undamped Systems | |
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| Underdamped Systems | |
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| Overdamped Systems | |
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| Critically Damped Systems | |
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| Coulomb Friction | |
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| Transient Response to Basic Excitations | |
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| Method of Undetermined Coefficients | |
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| Superposition and Time Delay | |
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| Pulse Excitation | |
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| Step and Impulse Responses | |
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| Shock Spectra | |
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| References and Selected Readings | |
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| Exercises | |
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| Steady-State Response to Harmonic Excitation | |
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| Complex Frequency Response | |
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| Power Dissipation | |
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| Quality Factor of Resonance | |
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| Structural Damping | |
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| Resonant Response | |
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| Rotating Imbalance | |
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| Basic Model | |
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| Frequency Response | |
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| Whirling of Shafts | |
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| Force Transmission | |
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| Periodic Excitations | |
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| Complex Fourier Series | |
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| The Discrete Fourier Transform | |
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| The Inverse Discrete Fourier Transform | |
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| Explanation and Implementation of the FFT Algorithm | |
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| Periodic Response Using FFTs | |
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| Accelerometers and Seismometers | |
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| Transient Response Revisited | |
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| Convolution Integral | |
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| FFTs for Transient Response | |
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| References and Selected Readings | |
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| Exercises | |
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| Modal Analysis of Multi-Degree-of-Freedom Systems | |
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| Background | |
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| Eigenvalue Problem--Undamped Systems | |
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| Natural Frequencies and Modes | |
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| Orthogonality and Normalization | |
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| Computerized Implementations | |
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| Flexibility Coefficients | |
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| Repeated Natural Frequencies | |
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| Rigid Body Modes | |
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| Modal Equations | |
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| Coordinate Transformations | |
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| Modal Coordinates | |
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| Modal Coordinate Description of Mechanical Energy and Power | |
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| Free Vibration Response | |
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| Forced Response | |
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| Modal Damping | |
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| Harmonic Steady-State Response | |
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| References and Selected Readings | |
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| Exercises | |
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| Harmonic Excitation of Multi-Degree-of-Freedom Systems | |
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| Frequency Domain Transfer Function | |
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| Structural Damping and Modal Analysis | |
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| Vibration Absorber | |
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| FFT Techniques | |
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| Analysis of Transient Response | |
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| Experimental Modal Analysis | |
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| References and Selected Readings | |
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| Exercises | |
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| Vibration of Elastic Bars: the Ritz Method and the Rayleigh Ratio | |
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| Equations of Motion | |
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| Axial Displacement | |
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| Torsion of Circular Bars | |
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| Flexural Displacement | |
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| Implementation and Solution | |
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| Eigensolutions | |
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| Modal Analysis | |
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| Orthogonality of the Mode Functions | |
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| Modal Response | |
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| Initial Conditions: The Expansion Theorem | |
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| Free Vibration | |
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| Impulse Response | |
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| Harmonic Steady-State Response | |
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| Rayleigh Ratio and Convergence Properties | |
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| Time-Dependent Boundary Conditions | |
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| Ritz Method for Discrete Systems | |
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| References and Selected Readings | |
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| Exercises | |
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| Field Descriptions for Vibrating Bars | |
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| Derivation of Motion Equations | |
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| Field Equations | |
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| Boundary Conditions | |
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| Eigensolutions for Extension and Torsion | |
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| Eigensolution for Flexure | |
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| Wave Interpretation of Modes and High-Frequency Asymptotics | |
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| Symmetry and Mode Functions | |
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| Orthogonality | |
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| Modal Analysis of Response | |
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| Modal Equations | |
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| Steady-State and Transient Response | |
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| Time-Dependent Boundary Conditions | |
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| Mindlin-Goodman Decomposition | |
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| Harmonic Boundary Excitation Wave Solution | |
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| Timoshenko Beam Theory | |
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| Field Equations | |
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| Wave Solutions | |
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| Modal Analysis | |
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| References and Selected Readings | |
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| Exercises | |
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| The Finite Element Method | |
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| Interpolating Functions | |
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| Elemental Matrices | |
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| Conversion to Global Coordinates | |
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| Assembly of the Elements | |
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| Reaction Forces and Constraint Conditions | |
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| References and Selected Readings | |
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| Exercises | |
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| Substructuring Concepts | |
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| Method of Lagrange Multipliers | |
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| Constraint Equations and Reactions | |
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| Synthesis of the Equations of Motion | |
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| Solution Methods | |
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| Component Mode Synthesis | |
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| Relaxation of Constraints | |
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| Component Properties | |
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| References and Selected Readings | |
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| Exercises | |
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| Damped Modal Analysis: the State Space | |
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| State-Space Equations | |
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| Eigenvalue Problem | |
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| Relation to Previous Developments | |
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| Orthogonality | |
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| Modal Coordinates | |
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| Free Vibration | |
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| Impulsive Forces | |
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| Steady-State Harmonic Vibration | |
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| Rigid Body Motion | |
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| Closure | |
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| References and Selected Readings | |
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| Exercises | |
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| Modal Analysis of Gyroscopic Systems | |
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| General Linearized Equations of Motion | |
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| Right and Left Eigenvalue Problems | |
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| Dynamic Stability | |
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| Bi-orthogonality and Modal Equations of Motion | |
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| Moving Continuous Systems | |
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| References and Selected Readings | |
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| Exercises | |
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| Introduction to Rotordynamics | |
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| Elements of a Rotordynamic Model | |
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| Effects of Internal and External Damping | |
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| Flexible Orthotropic Bearings | |
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| Gyroscopic Effects | |
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| Flexible Orthotropic Shafts | |
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| References and Selected Readings | |
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| Exercises | |
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| Lagrange's Equations | |
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| Transient Responses for Underdamped One-Degree-of-Freedom Systems | |
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| Deformation Modes for Uniform Bars | |
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| Index | |