THEORY OF VIBRATION
Course Objective:
To provide basic concept for the dynamics response analysis of common machines and machine components. To model a given system for a vibratory response. To develop computer simulation and program for the dynamic response
 Engine Force Analysis (2hours)
 Analytical Method for Velocity and Acceleration of the Piston and the Connecting Rod
 Equivalent Dynamical System
 Analytical Method for Inertia Torque
 Graphical Method for Velocity and Acceleration of the Piston and the Connecting Rod
 Turning Moment Diagram and Flywheel (2hours)
 Turning Moment Diagram
 Fluctuation of Energy and Coefficient of Fluctuation of Energy
 Flywheel
 Coefficient of Fluctuation of Speed
 Energy Stored in a Flywheel and Flywheel Sizing
 Gyroscopic Couple (3 hours)
 Precessional Angular Motion
 Gyroscopic Couple
 Effect of Gyroscopic Couple on Aeroplane
 Stability of a Four Wheel and Two Wheel Vehicles
 Effect of Gyroscopic Couple on a Disc Fixed Rigidly at a Certain Angle to a Rotating Shaft
 Governors (4 hours)
 Function of a Governer
 Terms Used in Governer
 Types of Governers
 Sensitiveness and Stability of Governors
 Balance of Machinery (6 hours)
 Balancing of a Single Rotating Mass by a Single Mass Rotating in the Same Plane
 Balancing of a Single Rotating Mass by Two Masses Rotating in Different Planes
 Balancing of Several Masses Rotating in the Same Plane
 Balancing of Several Masses Rotating in the Different Planes
 Types of Balancing Machines
 Balancing of Reciprocating Masses
 Balancing of Multicylinder Engines, Inline, Vtype, Opposed and Radial Configurations
 Balance of Four Bar Linkages
 Vibration of Single Degree of Freedom Systems (10 hours)
 Definition and Effects of Vibration, Terms Used in Vibration
 Elements of a Vibrating System
 Undamped Vibration of Single Degree of Freedom System
 Damped Vibration of Single Degree of Freedom System
 Forced Harmonic Response of Single Degree of Freedom System with Viscous Damping
 Systems with Coulomb Damping
 Rotating Unbalance
 Whirling of RotorShaft Systems
 Vibration Isolation and Force Transmissibility
 Response of Harmonic Excitation of Support
 Vibration Measuring Instruments
 Energy Dissipated by Damping
 Convolution Integral and General Force Excitation
 Vibration of Two Degree of Freedom Systems (4hours)
 Undamped Vibration of Two Degrees of Freedom System, Natural Frequencies and Mode Shapes
 Damped Vibration of Two Degrees of Freedom System
 Forced Harmonic Vibration of Two Degrees of Freedom System
 Vibration Absorber
 Vibration of Multi Degree of Freedom Systems (6 hours)
 Equations of Motion in Matrix Form
 Flexibility and Stiffness Matrices, Reciprocity Theorem
 Eigenvalues and Eigenvectors, Orthogonal Properties of Eigenvectors
 Modal Analysis
 General Forced Response
 Approximate Numerical Methods (4 hours)
 Rayleigh Method
 RayleighRitz Method
 Dunkerley Method
 Matrix Iteration Methods
 Finite Difference Method
 Vibration of Continuous Systems (4 hours)
 Lateral Vibration of a String
 Longitudinal Vibration in Rods
 Torsional Oscillation in Circular Shafts
 Lateral Vibration in Beams
Practical:
 Response of Governors
 Experiment on Gyroscope
 Balancing of Rotating Masses
 Response of a Spring Mass System
 Whirling of a Rotating Shaft
References:
 H. Mabie and C.F. Reinholtz, “Mechanisms and Dynamics of Machinery”, H, Wiely.
 W. T. Thomson, “Theory of Vibration with Applications”, Prentice Hall.
 S.S. Rao, “Mechanical Vibrations”, Addison Wesley.
 S. G. Kelly, “Fundamentals of Mechanical Vibrations”, McGraw Hill.
 A. Gilat, “MATLAB An Introduction with Applications”, Wiley India.
Evaluation Scheme:
There will be questions covering all the chapters of the syllabus. The evaluation scheme will be indicated in the table below:
Unit 
Chapter 
Topics 
Marks 
1 
1, 2 & 3 
All 
16 
2 
4 & 5 
All 
16 
3 
6 
All 
16 
4 
7 & 8 
All 
16 
5 
9 & 10 
All 
16 
Total 
80 
*Note: There may be minor deviation in marks distribution
