Mechanical Vibrations

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Overview of the course, practical applications and research trends,Harmonic and periodic motions, vibration terminology.
Single-DOF Free Vibrations:
Vibration model, Equation of motion-Natural Frequency,Energy method, Rayleigh method,Principle of virtual work, Damping models.
Viscously damped free vibration,Special cases: oscillatory, non-oscillatory and critically damped motions,Logarithmic decrement, Experimental determination of damping coefficient.
Forced harmonic vibration, Magnification factor,Rotor unbalance, Transmissibility,Vibration Isolation,Equivalent viscous damping, Sharpness of resonance.
Two-DOF Free Vibrations:
Generalized and Principal coordinates, derivation of equations of motion,Lagrange’s equation,Coordinate coupling,Forced Harmonic vibration.
Vibration Absorber:
Tuned absorber, determination of mass ratio,Tuned and damped absorber, unturned viscous damper.
Multi-DOF :
Derivation of equations of motion, influence coefficient method,Properties of vibrating systems: flexibility and stiffness matrices, reciprocity theorem,Modal analysis: undamped,Modal analysis: damped.
Calculation of natural frequencies:
Rayleigh method,Stodala method,Matrix iteration method,Holzer method and Dunkerley’s method.
Torsional vibration:
Simple systems with one or two rotor masses,Multi-DOF systems-transfer matrix method,Geared system,Branched system.
Continuous systems : closed form solutions:
Vibration of strings,Longitudinal and torsional vibration of rods,Transverse vibration of beams: equations of motion and boundary conditions,Transverse vibration of beams: natural frequencies and mode shapes.
Continuous systems : Approximate solutions:
Rayleigh’s energy method,Rayleigh-Ritz method,Assumed modes and Galerkin’s method.
Finite element analysis:
Finite element formulation for beams: Galerkin’s method,Beams elemental mass and stiffness matrices, Elemental force vector,Global finite element assembly and imposition of boundary conditions and solution procedure,Finite element formulation for rods.
Signature analysis and preventive maintenance:
Vibration testing equipments: signal generation, measuring and conditioning instruments,Vibration testing equipments: signal analysis instruments,Vibration signatures and standards,Field balancing of rotors.

Course Curriculum

Overview of the Course, Practical and Research Trends Details 1:2:52
Harmonic and Periodic Motions, Vibration Terminology Details 59:9
Vibration Model, Equation of Motion-Natural Frequency Details 59:6
Energy Method, Principle of Virtual Work Details 59:16
Viscously Damped Free Vibration Special Cases: Oscillatory Details 58:47
Logarithmic Decrement Experimental Determination of Damping Coefficient Hysteresis Loop Details 59:32
Coulomb Damping other Damping Models Details 55:23
Forced Harmonic Vibration, Magnification Factor Details 56:43
Laplace Transform, Superposition Theorem Details 58:27
Rotor Unbalance and Whirling of Shaft, Transmissibility Details 58:32
Support Motion, Vibration Isolation Details 59:38
Sharpness of Resonance, Vibration Measuring Instruments Details 58:35
Generalized and Principle Coordinates, Derivation of Equation of Motion Details 59:53
Lagranges’s Equation Details 59:23
Coordinate Coupling Details 1:18
Forced Harmonic Vibration Details 58:6
Tuned Absorber, Determination of Mass Ratio Details 59:29
Tuned and Damped Absorber, Untuned Viscous Damper Details 59:11
Modal Analysis: Undamped Details 59:5
Modal Analysis: Damped Details 59:1
Simple Systems With One Two or Three Discs Geared System Details 0:59
Multi-Degree of Freedom Systems-Transfer Matrix Method Branched System Details 1:2:25
Derivation of Equations of Motion Part 1-Newton’s and Hamilton’s Principle Details 58:24
Derivation of Equations of Motion Part 2-Newton’s and Hamilton’s Principle Details 59:53
Vibration of Strings Details 0:57
Longitudinal and Torsional Vibration of Rods Details 1:59
Transverse Vibration of Beams, Equations of Motion and Boundary Conditions Details 58:43
Transverse Vibration of Beams: Natural Frequencies and Mode Shapes Details 59:51
Rayleigh’s Energy Method Details 1:3
Matrix Iteration Method Details 1:11
Durkerley, Rayleigh-Ritz and Galerkin Method Details 58:54
Finite Element Formulation for Rods, Gear Train and Branched System Details 1:8:11
Finite Element Formulation for Beams: Galerkin’s Method Details 58:25
Global Finite Element Assembly and Imposition of Boundary Conditions Details 59:51
Vibration Testing Equipments: Signal Measurements Details 1:14
Vibration Testing Equipments: Signal Analysis Details 55:53
Field Balancing of Rotors Details 57:47
Condition Monitoring Details

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