# Vibrations of Plates and Shells

By Prof. Venkata R. Sonti   |   IISc Bangalore
Learners enrolled: 277
The course presents theory of vibrations of continuous systems such as rods, plates and shells. Many engineering applications like automobiles, aircraft structures, ship hulls, submarine hulls, pipes carrying water and all such applications where high speed moving parts are used, require knowledge of this topic as high vibrations will be a problem.

INTENDED AUDIENCE: Masters and PhD students

PREREQUISITES: Bachelors in engineering or science. A basic course in lumped vibrations is required.

INDUSTRY SUPPORT: Aircraft industry, automobile industry, home appliances like washing machines.
Summary
 Course Status : Completed Course Type : Elective Duration : 12 weeks Category : Mechanical Engineering Credit Points : 3 Level : Postgraduate Start Date : 25 Jul 2022 End Date : 14 Oct 2022 Enrollment Ends : 08 Aug 2022 Exam Date : 30 Oct 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week 1: Differential Geometry
Week 2: Differential length and strain
Week 3: Hamilton’s Law for vibrating shells
Week 4: The general equations of motion
Week 5: Equations of motion for a vibrating rectangular plate
Week 6: Modes and natural frequencies of vibrating structures and their animations
Week 7: Modes and natural frequencies of vibrating cylindrical shells
Week 8: The Rayleigh Ritz method for approximating natural frequencies and modeshapes
Week 9: The Rayleigh Ritz method applied to plates and shells
Week 10: Forced response of plates and shells using modal summation
Week 11: Forced response of a cylindrical shell
Week 12: Vibrations of connected structures: The Receptance method

### Books and references

1. Vibrations of Shells and Plates. Author: Werner Soedel

### Prof. Venkata R. Sonti

IISc Bangalore
Prof. Venkata Sonti has a Ph.D. from Purdue University (Herrick labs., 1994) with a specialization in acoustics and vibrations. He has been a faculty at the Indian Institute of Science since 1999 in the Dept. of Mechanical Engineering. He has been conducting research and teaching courses in vibrations, acoustics, linear and nonlinear sound-structure interaction for the last 22 years.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 30 October 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IISc Bangalore. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team