# ME 710: Vibrations Engineering

Description:
An in depth analysis of vibrations is done in the course, the latter part of the course focuses on actual applications and metrology. Starting off from simple single body vibrations the course extends up to vibrating plates and deformable bars and sheets. The course is not extravagantly mathematical and the professors try to keep the exams interesting. A lot of real life applications like the car suspension and airplane vibrations are discussed in detail in the class.

If you have completed ‘Kinematics and Dynamics of Machines’ (ME316 – KDoM), then things can be very easy to start off with, as it may seem a brisk repetition of the concepts already learnt. In fact, KDOM is a prerequisite for the course, but the professor is not very strict and taking up vibrations before KDOM would help a lot in KDOM.

The overall difficulty level would be on a higher side, especially in the mid part of the course, when differential equations reach their peak.

Course Contents:
1. Single degree of freedom vibrations
2. Multi degree of freedom Vibrations
3. Damping
4. Matrix form for multi degree vibrations
5. Modal analysis
6. Continuous systems
7. Energy and the Lagrange methods
8. Higher order differential equations
9. Vibrations of beams, bars, plates
10. Metrology and vibration measurement
11. Applications

Motivation and key learnings from the course:
Vibrations analysis is very important in design of machines. You will be taught the mathematics behind vibrations analysis and then jump into actual applications. The course will talk in detail about car suspension models and springs in general. Things and terms like ‘Quarter car and Half Car suspension model’ will become very clear. All these things are very relevant and you will clearly see their applications in engineering. A very relevant course for CADA students and those interested in the design aspect of engineering.

Key learnings would include solving differential equations, matrices and eigen value
solutions, and concepts on vibrations, energy methods calculations. The course will leave
everything explained with regards to the spring mass damper system.

References:
Your class notes, as simple as that. The professor will suggest a book on vibrations by S. S.
Rao, but will not stick to nomenclature. So things may get very difficult to understand if gone purely by the book. Also, a lot of material and animations will be uploaded on moodle. You can even try out solving equations on MATLAB and create animations and graphs. It would be a really good exercise to learn MATLAB if you are interested. The professor will suggest plotting of some graphs and give stuff as homework. A good advice would be to not leave this course for the last day of the exams, as apparently it looks simple on the surface, but the exams would test your concepts and not purely mathematical power. Solve all the sample questions the professor uploads before the exams. They may seem very difficult and lengthy but are very much like the questions asked in the exams.

(Written by Tej Vaidya)