Vibration of Continuous Systems

By Prof. Sudip Talukdar   |   IIT Guwahati
Learners enrolled: 78
All structures or mechanical systems are in fact, continuous having their physical parameters, external forces and their response are distributed in space. The dynamic behavior of the structures or machine components, can only be truly reflected in the continuous systems. The slenderness of the structures necessitates the adoption of continuous modelling. The exact solutions that can be obtained from continuous models provide true physical behavior in addition to yielding various bench mark results for testing the efficacy of many numerical methods used in discrete approaches. Keeping this in mind, the present course has been framed to teach the students about the formulation and solution of vibration problems of the continuous systems by exact method as well as by numerical techniques with application of MATLAB tool box. The course is designed for 12 modules in which each module will consist of 3 or 4 lecture hours.

INTENDED AUDIENCE: B.E Final year/M.Tech/ PhD students/Industrial persons

PREREQUISITES: BE/B.Tech in Civil/Mechanical/Aerospace Engg/ Marine Engg.

INDUSTRY SUPPORT: Aeronautics Research & Development Board, Delhi; Indian Space Research Org.,
Course Status : Upcoming
Course Type : Elective
Duration : 12 weeks
Start Date : 23 Jan 2023
End Date : 14 Apr 2023
Exam Date : 29 Apr 2023 IST
Enrollment Ends : 30 Jan 2023
Category :
  • Civil Engineering
Credit Points : 3
Level : Postgraduate

Page Visits

Course layout

Week 1:  Introduction to continuous system:
1. Modelling of undamped and damped system
2. Concepts of time domain and frequency domain approach
3. Generalized approach for forced vibration
Week 2: Different approaches for problem formulation
1. Equation of motion of continuous system by force balance
2. Energy approach and Hamilton’s principle
3. Lagranges equations and their applications.
Week 3: One dimensional wave equation:
1. D,Alembert solution of the wave equation
2. Transverse vibration of stretched string
3. Modal analysis and dynamic response of flexible string
Week 4: Axial and torsional vibration of bar:
1. Development of equation of motion by force balance and energy principle
2. Free vibration problems in axially loaded bar and torsional system,
3. Dynamic response of Shaft subjected to distributed couple or concentrated couple.
Week 5: Flexural vibration of beams:
1. Equation of motions of slender beams
2. Eigen value problems in beams
3. Forced vibration analysis using mode superposition techniques
Week 6: Vibration of beams subjected to moving load:
1. Formulation of problems in vibration of beams subject to moving load
2. Solution of Problems using mode superposition principles
3. Some practical applications
Week 7: Combination of continuous and lumped parameter system:
1. Exact solution of beam vibration with a concentrated mass
2. Semi-analytical approach for vibration of beams with several concentrated masses
3. Beam vibration problem with moving oscillator
Week 8: Vibration of membranes and plates:
1. Equation of motion for the vibration of stretched membranes
2. Vibration of rectangular plates
3. Practical applications of vibration of plates
Week 9: Approximate methods in vibration of continuous system:
1. Rayleigh-Ritz method
2. Gallerkin’s approach
3. Finite difference method in vibration of beams and plates.
Week 10: Vibration isolation:
1. Continuous system subject to support excitation
2. Force transmission and vibration isolation
3. Tuned mass damper for vibration reduction.
Week 11: Transient vibration analysis:
1. Unit impulse and response to arbitrary excitation
2. Response to step, ramp and pulse excitation 3. Dynamic analysis using ground motion data
Week 12: Numerical techniques with MATLAB applications:
1. Eigenvalues and eigen vector computation including state space form
2. Direct integration methods
3. Spectral analysis of structures for earthquake excitation

Books and references

1. Meriovitch, L (1986) “Elements of Vibration Analysis”, Mc Graw Hill Book Co., New York
2. Thompson, W. T (1990) “Theory of Vibration with applications”CBS Publishers, New Delhi
3. Inman, D (2014) “Engineering Vibration” Pearson, New Delhi
4. Hurty, W. C and Rubinstein (1967) M. F, “Dynamics of Structures”, Prentice Hall of India Pvt Ltd, New Delhi.
5. Fryba, L (2012), “Vibration of Solids and Structures under moving loads”, Springer.
6. Paz, M and Kim , Y. H (2018), “Structural Dynamics: Theory and Computation”, Springer

Instructor bio

Prof. Sudip Talukdar

IIT Guwahati
Prof. Sudip Talukdar is currently working as a faculty of Civil Engineering Department of Indian Institute of Technology Guwahati. Prior to joining IIT Guwahati, he was Assistant Professor in Civil Engineering at Regional Engineering College, Silchar (presently, NIT Silchar). He is specialized in Structural Engineering. He obtained his B.E from Regional Engineering College Silchar (presently NIT Silchar) with a gold medal. He completed his Masters in Structural Engineering from Department of Civil Engineering of Indian Institute of Technology Kharagpur and PhD from Indian Institute of Technology Kanpur in Structural Dynamics in Aerospace Engineering Department. He has 21 years of experience in teaching and research as faculty of Civil Engineering Department in IIT Guwahati and 16 years in Regional Engineering College Silchar. He has published 127 papers till date in reputed International/ National Journals and Conference Proceedings. His research area includes theoretical and experimental works in wide areas of Structural Engineering. He is a member of Institution of Engineers (Ind), Indian Road Congress and Indian Society of Theoretical and Applied mechanics.

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: 29 April 2023 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 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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