Finite element formulation for beams: Galerkins method, beams elemental mass and stiffness matrices, elemental force vector. 

1. Overview of the Course, Practical and Research Trends
2. Harmonic and Periodic Motions, Vibration Terminology
3. Vibration Model, Equation of Motion-Natural Frequency
4. Energy Method, Principle of Virtual Work
5. Viscously Damped Free Vibration Special Cases: Oscillatory, non-Oscillatory and Critically Damped Motions
6. Logarithmic Decrement Experimental Determination of Damping Coefficient Hystersis Loop
7. Coulomb Damping other Damping Models
8. Forced Harmonic Vibration, Magnification Factor
9. Laplace Transform, Superposition Theorem
10. Rotor Unbalance and Whirling of Shaft, Transmissibility
11. Support Motion, Vibration Isolation
12. Sharpness of Resonance, Vibration Measuring Instruments
13. Generalized and Principle Coordinates, Derivation of Equation of Motion
14. Lagranges's Equation
15. Coordinate Coupling
16. Forced Harmonic Vibration
17. Tuned Absorber, Determination of Mass Ratio
18. Tuned and Damped Absorber, Untuned Viscous Damper
19. Derivation of Equations of Motion, Influence Coefficient Method
20. Properties of Vibrating Systems: Flexibility & Stiffness Matrices, Reciprocity Theorem
21. Modal Analysis: Undamped
22. Modal Analysis: Damped
23. Simple Systems With One Two or Three Discs Geared System
24. Multi-Degree of Freedom Systems-Transfer Matrix Method Branched System
25. Derivation of Equations of Motion (Part I) and Hamilton's Principle
26. Derivation of Equations of Motion (Part II) and Hamilton's Principle
27. Vibration of Strings
28. Longitudinal and Torsional Vibration of Rods
29. Transverse Vibration of Beams, Equations of Motion and Boundary Conditions
30. Transverse Vibration of Beams: Natural Frequencies and Mode Shapes
31. Rayleigh's Energy Method
32. Matrix Iteration Method
33. Durkerley, Rayleigh-Ritz and Galerkin Method
34. Finite Element Formulation for Rods, Gear Train and Branched System
35. Finite Element Formulation for Beams
36. Global Finite Element Assembly and Imposition of Boundary Conditions and Solution Procedure
37. Vibration Testing Equipments: Signal Measurements
38. Vibration Testing Equipments: Signal Analysis
39. Field Balancing of Rotors
40. Condition Monitoring

In this course, Prof.Rajiv Tiwari gives 40 video lectures on Mechanical Vibrations.