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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.
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