Structural Vibration

By Prof. Arunasis Chakraborty | IIT Guwahati

Learners enrolled: 275 | Exam registration: 8

ABOUT THE COURSE:

The course introduces the basic concept of dynamic equilibrium, Degrees of freedom, and equation of motion at the beginning. Then the learners are introduced to the free vibration of the SDOF system with Viscous and Coulomb damping followed by forced vibration of the SDOF system. Then the half-power bandwidth technique, energy dissipation due to damping, and equivalent / rate-independent damping are introduced. It is followed by different methods of the numerical response evaluation, the response spectrum, and the preparation of the elastic design spectrum with the examples solved using MATLAB. Then the MDOF system is introduced with eigen solution based decoupling for modal superposition, time history analysis, and response spectrum analysis for the multistoried buildings are explained with examples in MATLAB. The free and forced vibration of a continuous system are also covered. At last, the dynamic analysis of a building using Finite Element software is demonstrated.

INTENDED AUDIENCE: UG Final Year Students, PG Students, and Research Scholars.

Summary

Course Status :	Upcoming
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Civil Engineering
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	20 Jan 2025
End Date :	11 Apr 2025
Enrollment Ends :	27 Jan 2025
Exam Registration Ends :	14 Feb 2025
Exam Date :	26 Apr 2025 IST

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

Page Visits

Course layout

Week 1:
Lecture 1 : Newton’s Law, D’Alembert Principle, Degree of Freedom
Lecture 2 : Equation of Motion, Simple Harmonic Motion.

Week 2:
Lecture 3 : Undamped Free Vibration, Solution, Natural Frequencies
Lecture 4 : Damped Free Vibration, Solution, Under Damped, Critical Damped, Overdamped system
Lecture 5 : Energy in Free Vibration, Viscous, and Coulomb Damping models, Logarithmic Decrement,

Week 3:
Lecture 6 : Vibration due to constant force and harmonic force, Numerical examples
Lecture 7 : Half power Bandwidth Technique, Response due to Support Motion, Force Transmission
Lecture 8 : Energy Dissipation, Equivalent Viscous Damping, Rate Independent Damping.

Week 4:
Lecture 9 : Impulse Response function, Duhamel’s Integral, Example using MATLAB
Lecture 10 : Response due to Step and Ramp force.
Lecture 11 : Response due to Rectangle and Half Sinusoidal pulse force
Lecture 12 : Response due to Arbitrary support motion

Week 5:
Lecture 13 : Numerical techniques, Implicit and Explicit methods, Central Difference, Example with MATLAB Coding
Lecture 14 : Newmark - ß algorithm, Example with MATLAB Coding
Lecture 15 : Wilson - ? algorithm, Example with MATLAB Coding

Week 6:
Lecture 16 : Concept on Response Spectrum, Tripartite Response Spectrum, Important Features.
Lecture 17 : Elastic Design Spectrum, spectrum-compatible earthquake
Lecture 18 : Numerical Example in MATLAB.

Week 7:
Lecture 19 : Hamilton Principle, Lagrange Equation
Lecture 20 : Coupled Equation of Motion
Lecture 21 : Rayleigh Damping, Caughey Damping, Non-Classical Damping.

Week 8:
Lecture 22 : Natural Frequencies and Mode shapes of MDOF system
Lecture 23 : Orthogonality of Modes, Normalization of Modes, Modal Expansion of displacement.
Lecture 24 : Free Vibration of a Damped MDOF system.

Week 9:
Lecture 25 : Response Analysis in the Time domain by modal superposition, Numerical Example in MATLAB
Lecture 26 : Response Analysis in the frequency domain, Numerical Example

Week 10:
Lecture 27 : Equation of Motions, Solution Strategy, example in MATLAB
Lecture 28 : Peak modal response, Modal combination rules - SRSS, CQC methods
Lecture 29 : Model reduction Technique: Static Condensation, Theory, and Example
Lecture 30 : Model reduction Technique: Dynamic Condensation, Theory, and Example in MATLAB

Week 11:
Lecture 31 : Free Vibration – Eigen value problem
Lecture 32 : The vibration of a beam under different support conditions
Lecture 33 : Rayleigh’s Quotient, Approximate Method - Rayleigh’s Energy Method
Lecture 34 : Forced Vibration of a beam

Week 12:
Lecture 35 : Introduction to FE software
Lecture 36 : Response Spectrum Analysis of a multistoried building using FE software
Lecture 37 : Time History Analysis of a Multistoried building using FE software

Books and references

1. Clough W. R & Penzien J. Dynamics of Structures, Computers & Structures, Inc., Berkeley, USA,2003.
2. Paz M. Structural Dynamics Theory and Computation, CBS Publishers, New Delhi, 1987.
3. Meirovitch L. Analytical Dynamics, Dover Publication Inc., Mineola, New York, 2003.
4. Rao D. & Rao V. G. Elements of Structural Dynamics, John Wiley, Chennai, India, 2012.
5. Mukhopadhyay M. Structural Dynamics Vibration & Systems, Ane Books Pvt. Ltd. New Deihi, India, 2016
6. Chopra K. A. Dynamics of Structures, Pearson, 2012.

Instructor bio

Prof. Arunasis Chakraborty

IIT Guwahati

Prof. Arunasis Chakraborty has been associated with IIT Guwahati since 2009 where he is currently serving as a Professor in the Department of Civil Engineering and Center for Disaster Management & Research. His major areas of research include uncertainty quantification & reliability analysis, condition assessment, vibration control and wind energy. Dr. Chakraborty published in various peer reviewed international journals and conferences. He also participated in joint research and development projects with other academic institutions, government agencies and high-tech industries that included Rice University, Chalmers University, BRNS, DST, NPCIL, BRO, NF Railway among many others.

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: April 26, 2025 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

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

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 Guwahati .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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