INTRODUCTION: Types of vibrations, Simple Harmonic Motion (S.H.M),
principle of super position applied to Simple Harmonic Motions. Beats,
Fourier theorem and simple problems.
UNIT II:
UNDAMPED FREE VIBRATIONS: Single degree of freedom systems.
Mass Undamped free vibration-natural frequency of free vibration, stiffness
of spring elements, effect of mass of spring, Compound Pendulum.
UNIT III:
DAMPED FREE VIBRATIONS: Single degree freedom systems, different
types of damping, concept of critical damping and its importance, study of
response of viscous damped systems for cases of under damping, critical and
over damping, Logarithmic decrement.
UNIT IV:
FORCED VIBRATION: Single degree freedom systems, steady state
solution with viscous damping due to harmonic force. Solution by Complex
algebra, Reciprocating and rotating unbalance, vibration isolationtransmissibility
ratio. Due to harmonic exitation and support motion.
PART – B
UNIT V:
VIBRATION MEASURING INSTRUMENTS & WHIRLING OFSHAFTS: Vibrometer meter and accelerometer. Whirling of shafts with and
without air damping. Discussion of speeds above and below critical speeds.
UNIT VI:
SYSTEMS WITH TWO DEGREES OF FREEDOM: Introduction,
principle modes and Normal modes of vibration, co-ordinate coupling,
generalized and principal co-ordinates, Free vibration in terms of initial
conditions. Geared systems. Forced Oscillations-Harmonic excitation.
Applications: a) Vehicle suspension. b) Dynamic vibration absorber.
c) Dynamics of reciprocating Engines.
UNIT VII:
CONTINUOUS SYSTEMS: Introduction, vibration of string, longitudinal
vibration of rods, Torsional vibration of rods, Euler’s equation for beams.
UNIT VIII:
NUMERICAL METHODS FOR MULTI DEGREE FREEDOMSYSTEMS: Introduction, Influence coefficients, Maxwell reciprocal
theorem, Dunkerley’s equation. Orthogonality of principal modes, Method of
matrix iteration-Method of determination of all the natural frequencies using
sweeping matrix and Orthogonality principle. Holzer’s method, Stodola
method
REFERENCE
TEXT BOOKS:
1. Theory of Vibration with Applications: W.T. Thomson and Marie
Dillon Dahleh, Pearson Education 5th edition, 2007.
2. Mechanical Vibrations: V.P. Singh, Dhanpat Rai & Company Pvt.
Ltd., 3rd edition, 2006
Reference Books
1. Mechanical Vibrations: S.S. Rao, Pearson Education Inc, 4th
Edition, 2003.
2. Mechanical Vibrations: S. Graham Kelly, Schaum’s Outline
Series, Tata McGraw Hill, Special Indian edition, 2007.
3. Theory & Practice of Mechanical vibrations: J.S. Rao & K.
Gupta, New Age International Publications, New Delhi, 2001.
4. Elements of Vibrations Analysis: Leonanrd Meirovitch, Tata
McGraw Hill, Special Indian edition, 2007.