Introduction 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.
