Mechanical Vibrations

Overview

Contents:
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,Lagranges 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 Dunkerleys 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:
Rayleighs energy method,Rayleigh-Ritz method,Assumed modes and Galerkins method.
Finite element analysis:
Finite element formulation for beams: Galerkins 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.