Mechanical Vibrations

• Introduction, Classification of Vibration Systems, Harmonic motion, Vector representation of harmonic motion, Natural frequency & response, Effects of vibration, superposition of simple harmonic motions, beats, Fourier analysis‐analytical method.
• Single Degree Freedom System, Equation of motion, Newton’s method, D’Alembert’s principle, Energy method etc., Free vibration, Natural frequency, Equivalent systems, Displacement, Velocity and acceleration, Response to an initial disturbance, Torsional vibrations, Damped vibrations, Vibrations of systems with viscous damping, Logarithmic decrement, Energy dissipation in viscous damping.

Single Degree Freedom: Forced Vibration Forced vibration, Harmonic excitation with viscous damping, steady state vibrations, Forced vibrations with rotating and reciprocating unbalance, Support excitation, Vibration isolation, Transmissibility, Vibration measuring instruments, Displacement, velocity, and acceleration measuring instruments

Two Degree Freedom systems Introduction, Principal modes, Double pendulum, Torsional system withdamping, Coupled system, Principle of vibration absorber, Undamped dynamic vibration absorbers,Torsional vibration absorber, Centrifugal pendulum absorbers, Vibration isolators and Dampers.

Multi‐degree Freedom system: Exact Analysis, Undamped free and forced vibrations of multi‐degree freedom systems, influence coefficients, Reciprocal theorem, Torsional vibration of multi‐degree rotor system, Vibration of gear system, Principal coordinates, Continuous systems‐ Longitudinal vibrations of bars, Torsional vibrations of circular shafts. Multi Degree Freedom system: Numerical Analysis by Rayleigh’s method, Dunkerley’s, Holzer’s and Stools methods, Rayleigh‐Ritz method.

Critical speed of shafts, Whirling of uniform shaft, Shaft with one disc with and without damping, Multi‐disc shafts, Secondary critical speed. Industrial case studies (any two) involving mechanical vibrations, their impact and performance analysis. Introduction to the vibration analysis using MATLAB.