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

1. Engine Force Analysis (2hours)
1. Analytical Method for Velocity and Acceleration of the Piston and the Connecting Rod
2. Equivalent Dynamical System
3. Analytical Method for Inertia Torque
4. Graphical Method for Velocity and Acceleration of the Piston and the Connecting Rod
2. Turning Moment Diagram and Flywheel (2hours)
1. Turning Moment Diagram
2. Fluctuation of Energy and Coefficient of Fluctuation of Energy
3. Flywheel
4. Coefficient of Fluctuation of Speed
5. Energy Stored in a Flywheel and Flywheel Sizing
3. Gyroscopic Couple (3 hours)
1. Precessional Angular Motion
2. Gyroscopic Couple
3. Effect of Gyroscopic Couple on Aeroplane
4. Stability of a Four Wheel and Two Wheel Vehicles
5. Effect of Gyroscopic Couple on a Disc Fixed Rigidly at a Certain Angle to a Rotating Shaft
4. Governors (4 hours)
1. Function of a Governer
2. Terms Used in Governer
3. Types of Governers
4. Sensitiveness and Stability of Governors
5. Balance of Machinery (6 hours)
1. Balancing of a Single Rotating Mass by a Single Mass Rotating in the Same Plane
2. Balancing of a Single Rotating Mass by Two Masses Rotating in Different Planes
3. Balancing of Several Masses Rotating in the Same Plane
4. Balancing of Several Masses Rotating in the Different Planes
5. Types of Balancing Machines
6. Balancing of Reciprocating Masses
7. Balancing of Multicylinder Engines, In-line, V-type, Opposed and Radial Configurations
8. Balance of Four Bar Linkages
6. Vibration of Single Degree of Freedom Systems (10 hours)
1. Definition and Effects of Vibration, Terms Used in Vibration
2. Elements of a Vibrating System
3. Undamped Vibration of Single Degree of Freedom System
4. Damped Vibration of Single Degree of Freedom System
5. Forced Harmonic Response of Single Degree of Freedom System with Viscous Damping
6. Systems with Coulomb Damping
7. Rotating Unbalance
8. Whirling of Rotor-Shaft Systems
9. Vibration Isolation and Force Transmissibility
10. Response of Harmonic Excitation of Support
11. Vibration Measuring Instruments
12. Energy Dissipated by Damping
13. Convolution Integral and General Force Excitation
7. Vibration of Two Degree of Freedom Systems (4hours)
1. Undamped Vibration of Two Degrees of Freedom System, Natural Frequencies and Mode Shapes
2. Damped Vibration of Two Degrees of Freedom System
3. Forced Harmonic Vibration of Two Degrees of Freedom System
4. Vibration Absorber
8. Vibration of Multi Degree of Freedom Systems (6 hours)
1. Equations of Motion in Matrix Form
2. Flexibility and Stiffness Matrices, Reciprocity Theorem
3. Eigenvalues and Eigenvectors, Orthogonal Properties of Eigenvectors
4. Modal Analysis
5. General Forced Response
9. Approximate Numerical Methods (4 hours)
1. Rayleigh Method
2. Rayleigh-Ritz Method
3. Dunkerley Method
4. Matrix Iteration Methods
5. Finite Difference Method
10. Vibration of Continuous Systems (4 hours)
1. Lateral Vibration of a String
2. Longitudinal Vibration in Rods
3. Torsional Oscillation in Circular Shafts
4. Lateral Vibration in Beams

Practical:

1. Response of Governors
2. Experiment on Gyroscope
3. Balancing of Rotating Masses
4. Response of a Spring Mass System
5. Whirling of a Rotating Shaft

References:

1. H. Mabie and C.F. Reinholtz, “Mechanisms and Dynamics of Machinery”, H, Wiely.
2. W. T. Thomson, “Theory of Vibration with Applications”, Prentice Hall.
3. S.S. Rao, “Mechanical Vibrations”, Addison Wesley.
4. S. G. Kelly, “Fundamentals of Mechanical Vibrations”, McGraw Hill.
5. 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: