MV (B-TECH Mechanical Engineering 7-8th)

Unit I Fundamentals : Importance of Study of Vibrations, Classifications of Vibrations, Free

and Forced, Undamped and Damped, Linear and Non-linear, Deterministic and Random,

Harmonic Motion, Vector and Complex Number Representations, Definitions and

Terminology, Periodic Functions, Harmonic Analysis, Fourier Series Expansion.

Unit II Free and Damped Vibrations : Single Degree of Freedom system, D’Alemberts

Principal, Energy Methods, Rayleighs Method, Application of these Methods, Damped

Free Vibrations, Logarithmic Decrement, Under Damping, Critical and Over Damping,

Coulomb Damping.

Unit III Harmonically Excited Vibrations : Forced Damped Harmonic Vibration of Single

Degree of Freedom Systems, Rotating Unbalance, Rotor Unbalance, Critical Speeds and

Whirling of Rotating Shafts, Support Motion, Vibration Isolation, Energy Dissipated by

Damping, Equivalent, Viscous Camping, Structural Damping Sharpness of Resonance,

Vibration Measuring Instruments.

Unit IV Transient Vibrations : Impulse Excitation, Arbitrary Excitation, Response to Step

Excitions, Base Excitation Solution by Laplace Transforms, Response Spectrum, RungeKutta

Method.

Unit V Two Degrees of Freedom Systems : Introduction to Multi-Degree of Freedom Systems,

Normal Mode Vibrations, Coordinate Coupling, Principal Coordinates, Free Vibrations in

Terms of Initial Conditions, Forced Harmonic Vibrations, Vibration Absorber,

Centrifugal Vibration Absorber, Vibration Damper.

Unit VI Multi degrees of Freedom Systems and Numerical Methods Introduction, Influence

Coefficients, Stiffness Matrix, Flexibility Matrix, Natural Frequencies and Normal

Modes, Orthogonality of Normal Modes, Dunkerley’s Equation, Method of Matrix

Iteration, The Holzer Type Problem, Geared and Branched Systems, Beams.

Unit VII Normal Mode Vibration of Continuous System: Vibrating String, Longitudinal

Vibrations of Rod, Torsional Vibrations of Rod, Lateral Vibrations of Beam.