B.Tech. IV Sem CIVIL Engineering

IV SEMESTER

4CE6.2. THEORY OF VIBRATIONS

 

UNIT 1
Undamped Free Vibrations of Single Degree of Freedom Systems:
Springs in parallel or in series, Newtons law of motion, free body diagram, D’Alembert’s principle, solution of differential equation of motion, Torsional vibration Frequency, Period, amplitude of vibration, Energy Methods.


UNIT 2
Damped Free Vibrations of Single degree of Freedom systems:
Different types of damping, Free vibration with Viscous damping, over damped systems, undreamed systems and critically damped systems. Logarithmic decrement.


UNIT 3
Forced Vibrations of Single Degree of Freedom Systems:
Forced vibrations with constant harmonic excitation, steady state and transient vibrations, resonance. Forced vibration with rotating & reciprocating unbalance masse. Forced vibrations due to excitation of support, absolute amplitude & relative amplitude, vibration isolation and transmissibility. Force transmitted to the foundation Seismic instruments.


UNIT 4
Two degrees of Freedom Systems:
Principal modes of vibration, solution of differential equations for a two degree of freedom system. Dynamic analysis of Continuous systems: Flexural vibration of uniform beams. Solution of equation of motion in free vibration. Natural frequencies & mode shoebox for systems uniforms beams.


UNIT 5
Multi degrees of Freedom:
Vibrations of a beam with point loads, U.D.L./Application of numerical methods. Rayleighs method, Dunkerley’s Method. Rayleigh-Ritz Method.