Vibrations of Structures

By Prof. Anirvan DasGupta   |   IIT Kharagpur
Learners enrolled: 671
All mechanical structures have flexibility, which becomes apparent under loading, more prominently under dynamic loading. It is of fundamental importance to understand the vibration characteristics of a structure in order to appropriately design systems subjected to dynamic loading in order to avoid/enhance resonance, sound generation and transmission, and fatigue failure. This course will expose the different modeling and analysis techniques for continuous systems such as strings, bars, beams and plates. Special emphasis is given to variational and approximate methods, which are useful for handling complex systems. The course is expected to be useful for both academic research and industrial applications, and will provide a stepping stone for more specialized and advanced courses.

INTENDED AUDIENCE  : Core for PG specializations in Mechanical, Civil and Aerospace. Elective for UG.
PRE-REQUISITES  :  Engineering Mathematics,Dynamics of Machines
INDUSTRIES SUPPORT : Automotive, aerospace, process industries etc.
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Category :
  • Mechanical Engineering
  • Advanced Dynamics and Vibration
  • Advanced Mechanics
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 18 Jan 2021
End Date : 09 Apr 2021
Enrollment Ends : 01 Feb 2021
Exam Date : 25 Apr 2021 IST

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

Page Visits

Course layout

Module 1 (Vibrations of strings and bars)
• Transverse Vibrations of Strings – I 
• Transverse Vibrations of Strings – II 
• Axial and Torsional Vibrations of Bars 
• Variational Formulation – I 
• Variational Formulation – II 
• Modal Analysis - I 
• Modal Analysis - II 
• Properties of Eigenvalue Problem
• Modal Analysis: Approximate Methods - I 
• Modal Analysis: Approximate Methods - II 
• The Initial Value Problem
• Forced Vibration Analysis – I 
• Forced Vibration Analysis – II 
• Forced Vibration Analysis – III 
• Damping in Structures
• Tutorial video - I

Module 2 (Vibrations of beams)
• Beam Models - I 
• Beam Models - II
• Modal Analysis of Beams 
• Applications of Modal Solution 
• Approximate Methods 
• Topic in Beam Vibration - I 
• Topic in Beam Vibration - II 
• Dynamics of Curved Beams 
• Vibrations of Rings and Arches
• Tutorial video - II

Module 3 (Vibrations of membranes)
• Dynamics of Membranes
• Vibrations of Rectangular Membrane
• Vibrations of Circular Membrane 
• Tutorial video - III

Module 4 (Vibrations of plates)
• Dynamics of Plates
• Vibrations of Rectangular Plates 
• Vibrations of Circular Plates
• Special Problems in Plate Vibrations 
• Tutorial video - IV

Books and references

1. Vibrations and waves in continuous mechanical systems, P. Hagedorn and A. DasGupta, John Wiley, Chichester, 2007
2. NPTEL web course Vibrations of Structures, A. DasGupt

Instructor bio

Prof. Anirvan DasGupta

IIT Kharagpur
Dr. Anirvan DasGupta is a faculty in Mechanical Engineering at IIT Kharagpursince 1999. His interests are in the mechanics of discrete and continuous systems.He has extensively taught courses at undergraduate and postgraduate levels likeMechanics, Kinematics of Machines, Dynamics, Dynamics of Machines, VibrationAnalysis, Wave Propagation in Continuous Media, and Rail Vehicle Dynamics.

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: 25 April 2021 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.


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 IIT Kharagpur .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

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