1 Introduction to Vibration -- 1. Introductory Remarks -- 2. Single Degree of Freedom Systems: Equations of Motion and Types of Problem -- 3. Response -- 4. General Structures: Equations of Motion -- 5. Response -- 6. Dynamic Interaction Problems -- 2 Free Vibration, Resonance and Damping -- 1. Introduction -- 2. Spring-Mass System -- 3. Simple Pendulum -- 4. Beam with Central Load -- 5. Rolling of a Ship -- 6. Springs in Parallel -- 7. Springs in Series -- 8. Free Vibration -- 9. Energy of Vibrating System -- 10. Damped Free Vibration -- 11. Undamped Forced Response -- 12. Damped Forced Response -- 13. Undamped Transient Vibration -- 14. Damped Transient Vibration -- 15. Summary of Results -- 3 Vibrations of Multi-Degree of Freedom Systems -- 1. Introduction -- 2. Free Vibrations of Two Degree of Freedom Systems -- 3. Free Vibrations of a Multi-Degree of Freedom System -- 4. Orthogonality of Mode Shapes -- 5. Modal Decomposition -- 6. Damped Free Vibrations of Multi-Degree of Freedom Systems -- 7. Forced Vibrations of Multi-Degree of Freedom Systems -- 4 Eigenvalue-Eigenvector Solution -- 1. Introduction -- 2. Three Degree of Freedom System -- 3. Zeros of Determinants -- 4. Banded and Symmetric Matrices -- 5. Reduction of Eigenvalue Equation to Standard Form -- 6. Solution of Standard Eigenvalue Equations by Stürm Sequence Technique -- 7. Solution of the Original Equations using Stürm Sequence Technique -- 8. Simultaneous Iteration -- 9. Comparison of Eigenvalue Solution Methods -- 10. Node Condensation -- 11. Substructure Analysis -- 12. Rate of Change of Eigenvalues -- 5 Approximate Methods for Calculating Natural Frequencies and Dynamic Response of Elastic Systems -- 1. Equivalent One Degree of Freedom Systems -- 2. Continuous Beams -- 3. Distribution Methods -- 4. Multi-Storey Frames -- 6 Determination of Response -- 1. Introductory Remarks -- 2. Steady State Response -- 3. Damping -- 4. Truncation of Series Solution -- 5. Response Spectrum Methods -- 7 The Finite Element Technique -- 1. Introduction -- 2. The Principle of Virtual Displacements -- 3. Finite Element Discretization and Element Matrices -- 4. System Equations -- 5. Solution -- 8 Two Dimensional and Plate Bending Applications -- 1. Introduction -- 2. In-Plane Plate Elements -- 3. In-Plane Vibration of Plates -- 4. Plate Bending Elements -- 5. Transverse Vibration of Plates -- 6. Combination of Plate and Beam Elements -- 9 Transient Response of Structures -- 1. Introduction -- 2. Transient Response without Damping -- 3. Damping -- 4. Damped Transient Response -- 5. Numerical Methods -- 10 Machine Foundations -- 1. Introduction -- 2. Transmissibility of a Foundation on a Rigid Base -- 3. Transmissibility of a Foundation on a Flexible Base -- 4. Low Tuned and High Tuned Foundations -- 5. Dynamic Absorber -- 6. Damped Dynamic Absorber -- 7. Design Codes -- 8. Steel Foundations for Turbo-Alternators -- 9. Conclusions -- 11 Vibration of Axi-Symmetric Shells -- 1. Introduction -- 2. Novozhilov's Thin Shell Theory -- 3. Finite Element Displacement Method applied to Axi-Symmetric Shells -- 4. Vibration Applications -- 5. Example -- Appendix. Matrices used in the Text -- 12 Some Recent Advances in Structural Vibration -- 1. Introductory Remarks -- 2. Direct Integration Methods -- 3. Accuracy -- 4. Non-linear Problems -- 5. Partitioning -- 13 Fluid Structure Interaction Problems -- 1. Introduction -- 2. The Mechanics of Drag, Inertia and Lift -- 3. Total Hydrodynamic Forces -- 4. Final Remarks -- 14 Introduction to Random Vibrations -- 1. Random Processes -- 2. Spectral Density Function -- 3. The Weiner-Khinchin Relationship -- 4. Response of a Single Spring System to Random Load -- 15 Earthquake Response of Structures -- 1. Introduction -- 2. Beam Analysis -- 3. Spectral Density of Response -- 16 Response of Structures to Wind Loading -- 1. Introduction -- 2. Response of Shells -- 17 Random Response Analysis of Off-Shore Structures -- 1. Introduction -- 2. One Degree of Freedom System -- 3. Multi-Degree of Freedom System -- 4. Closing Remarks.