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Vibrations of Engineering Structures


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Table of Contents

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 Sturm Sequence Technique.- 7. Solution of the Original Equations using Sturm 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.

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