18AE56 Theory of Vibrations syllabus for AE

Introduction: Types of vibrations, S.H.M, principle of super position applied to Simple Harmonic Motions. Beats, Fourier theorem and simple problems.

Undamped Free Vibrations: Single degree of freedom systems. Undamped free vibration, natural frequency of free vibration, Spring and Mass elements, effect of mass of spring, Compound Pendulum.

Damped Free Vibrations: Single degree of 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.

Forced Vibration: Single degree of 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.

Vibration Measuring Instruments & Whirling of Shafts: Vibration of elastic bodies – Vibration of strings – Longitudinal, lateral and torsional Vibrations.

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: Vehicle suspension, Dynamic vibration absorber and Dynamics of reciprocating Engines.

Continuous Systems: Introduction, vibration of string, longitudinal vibration of rods, Torsional vibration of rods, Euler’s equation for beams.

Numerical Methods for Multi-Degree 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.

Course Outcomes:

At the end of the course the student will be able to:

1. CO1: Apply the principle of super position to Simple Harmonic Motions.

2. CO2: Determine the vibrations using vibration instruments.

3. CO3: Analyze the multi-degree freedom systems.

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub- questions) from each module.
• Each full question will have sub- question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.

Textbook/s

1 Theory of Vibration with Applications W.T. Thomson and Marie Dillon Dahleh Pearson Education 5th edition, 2008

2 Mechanical Vibrations V.P. Singh DhanpatRai& Company Pvt. Ltd 2016

Reference Books

1 Mechanical Vibrations S.S. Rao Pearson Education Inc 4th Edition,2003

2 Mechanical Vibrations S. Graham Kelly 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.