Nonlinear Vibration Course | IIT Guwahati NPTEL | Prof. S.K. Dwivedy
Course Details
| Exam Registration | 27 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | Mechanical Engineering, Advanced Dynamics and Vibration |
| Credit Points | 3 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 26 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Beyond Linearity: Unlocking the Complex World of Nonlinear Vibration
In the realm of mechanical engineering and dynamics, the assumption of linearity has long been a convenient simplification. However, the true behavior of most real-world vibrating systems—from aerospace structures and automotive components to robotic manipulators and biomedical devices—is inherently nonlinear. To accurately predict, analyze, and control these systems, a deep understanding of nonlinear vibration is essential.
We are proud to present a comprehensive, 12-week course on Nonlinear Vibration, meticulously designed and taught by Prof. S. K. Dwivedy of the Indian Institute of Technology Guwahati. This course moves beyond textbook simplifications to equip you with the tools needed to tackle the fascinating complexities of real-world dynamic systems.
Meet Your Instructor: Prof. S. K. Dwivedy
Prof. Dwivedy brings over two decades of dedicated teaching and pioneering research in nonlinear dynamics to this course. His journey in this field began during his PhD at IIT Kharagpur, and for the last 20 years, he has been shaping minds at IIT Guwahati. A recognized expert, he has developed the web and video courses on Nonlinear Vibration for the National Programme on Technology Enhanced Learning (NPTEL).
His extensive research portfolio includes guiding 10 PhD and over 40 M.Tech students, along with publishing more than 150 papers in international journals and conferences. His work spans diverse and cutting-edge applications, including:
- Structural dynamics and vibration absorbers
- Energy harvesting systems
- Robotic manipulators
- Metallic ion polymer composites and pneumatic artificial muscles
- Biomedical applications of vibration control
Course Overview: What You Will Learn
This is a simulation-based course designed to help you visualize and understand the dynamic response of mechanical systems under various resonance conditions. The curriculum is structured to build from fundamental concepts to advanced applications.
Duration: 12 Weeks
Level: Undergraduate/Postgraduate
Categories: Mechanical Engineering, Advanced Dynamics and Vibration
Detailed Course Layout
| Week | Module & Topics |
|---|---|
| Week 1 | Module 1: Introduction Introduction to nonlinear mechanical systems, failure of superposition, Duffing and van der Pol’s equations, equilibrium points. |
| Week 2 | Module 2: Equation Development Developing equations of motion using symbolic software, Lagrange’s and Hamilton’s principles. |
| Weeks 3-4 | Module 3: Solution Methods Numerical solutions, Harmonic Balance, Method of Averaging, Method of Multiple Scales. |
| Week 5 | Module 4: SDOF Systems (Weak Excitation) Free and forced vibration of damped/undamped systems with nonlinearities. |
| Week 6 | Module 4: SDOF Systems (Hard Excitation) Super/sub-harmonic resonance, bifurcation analysis of fixed-point response. |
| Week 7 | Module 5: Parametric Excitation Principal/combination resonance, Floquet theory, frequency response. |
| Week 8 | Module 6: Complex Dynamics Stability analysis, quasi-periodic and chaotic system analysis. |
| Week 9 | Module 7: Numerical Methods Solving ODEs/DDEs, phase portraits, Poincaré sections, FFT, Lyapunov exponents. |
| Week 10 | Practical Application 1: Nonlinear Vibration Absorber Equation development, solution using Harmonic Balance, programming time/frequency response. |
| Week 11 | Practical Application 2: Nonlinear Energy Harvester Development and solution of EOM using the Method of Multiple Scales. |
| Week 12 | Practical Application 3: Electro-Mechanical System Analysis of parametric instability, study of periodic, quasiperiodic, and chaotic response. |
Who Should Enroll?
This course is invaluable for:
- Senior Undergraduate & Postgraduate Students in Mechanical Engineering and related fields.
- PhD Scholars conducting research in dynamics, vibrations, and control.
- Practicing Engineers in industries such as automotive, aerospace, manufacturing, and robotics who need to solve complex vibration problems to improve product design, durability, and performance.
Industry Relevance
Understanding nonlinear vibration is critical for innovation and problem-solving in modern industry. This course provides the analytical foundation needed to:
- Design more efficient and robust vibration absorbers.
- Develop high-performance energy harvesting devices.
- Analyze and mitigate chaotic vibrations in mechanical systems.
- Improve the dynamic performance and safety of aerospace and automotive structures.
All industries dealing with dynamic systems—manufacturing, automobile, aerospace, robotics, and biomedical engineering—will benefit from the skills taught in this course.
Recommended Textbooks & Resources
- Nayfeh & Mook, Nonlinear Oscillations
- Cartmell, Introduction to Linear, Parametric, and Nonlinear Vibrations
- Nayfeh & Balachandran, Applied Nonlinear Dynamics
- Seydel, From Equilibrium to Chaos
- Moon, Chaotic & Fractal Dynamics
- Rand, Lecture Notes on Nonlinear Vibrations (Online)
- Guckenheimer & Holmes, Nonlinear Oscillations...
- Strogatz, Nonlinear Dynamics and Chaos
Embark on this 12-week journey to master the principles and applications of nonlinear vibration. Under the expert guidance of Prof. S. K. Dwivedy, you will gain not just theoretical knowledge but also practical, simulation-based skills to analyze and solve the dynamic challenges of tomorrow's engineering world.
Enroll Now →