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Course Detail

Course Name Mechanical Vibrations
Course Code 15MEC404
Program B. Tech. in Mechanical Engineering
Semester Seven
Year Taught 2019


Unit 1

Introduction: Types of vibrations, Simple Harmonic Motion (SHM), principle of super position applied to Simple Harmonic Motions. Beats, Fourier theorem and simple problems.

Un-damped free vibrations: Single degree of freedom systems. Un-damped free vibration-natural frequency of free vibration, stiffness of spring elements, effect of mass of spring, Compound Pendulum.

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 2

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 isolation – transmissibility ratio. Due to harmonic excitation and support motion, Whirling of Shafts – Whirling of shafts with and without air damping, Discussion of speeds above and below critical speeds.

Vibration measuring instruments & Vibration Control: Vibration exciters, vibrometer and accelerometer, free & forced vibration tests, vibration isolation, vibration absorbers.

Unit 3

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.

Multi degree of freedom systems: 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. Rayleigh’s method.

Text Books

  1. W. T. Thomson and Marie Dillon Dahleh – ‘Theory of Vibration with Applications’ – Pearson Education – 2007 – 5th Edition
  2. S. S. Rao – ‘Mechanical Vibrations’ – Pearson Education Inc. – 2011 – 5th Edition


  • V. P. Singh, – ‘Mechanical Vibrations’ – Dhanpat Rai & Company Pvt. Ltd. – 2014 – 3rd Edition
  • S. Graham Kelly – ‘Mechanical Vibrations’ – Schaum’s Outline Series – Tata McGraw Hill – 2011 – Special Indian Edition
  • Leonanrd Meirovitch – ‘Elements of Vibrations Analysis’ – Tata McGraw Hill – 2007 – Special Indian Edition

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