# Wave Propagation through Periodic Structures and Metamaterials

- Institution: IIT Delhi
- Department: Civil Engineering
- Teacher: Prof. Arnab Banerjee
- Level: Graduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/105102001)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/105102001)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course offers a comprehensive exploration of wave propagation and metamaterial mechanics, beginning with the origins, classifications, and applications of metamaterials. It introduces foundational wave concepts in 1D monoatomic chains, delves into bandgap formation, and advances to complex systems like mass-in-mass and inertial amplifiers, emphasizing negative mass and stiffness phenomena. Students will study mono-coupled and beyond-nearest-neighbour systems, including roton-like features and transmittance behaviour in finite and infinite chains. The course also covers the role of damping, both Rayleigh and generalized models in 1D discrete systems. A major portion is dedicated to dynamic stiffness formulations and spectral element methods for bars, beams, frames, and thin-walled structures, along with comparison of spectral element and transfer matrix techniques. Advanced topics include wave coupling, group and phase velocities, energy flow, characteristic impedance, and wave behaviour in 2D lattice structures, including homogenization approaches for continuum modelling.

Intended audience: M. Tech or PhD students working on wave propagation and vibration attenuation

Prerequisites: Basic mechanical vibration courses and a desire to expand the horizon of knowledge in vibration control (UG courses on Mechanical Vibrations)

## Lectures

1. [Introduction to periodic structures and metamaterials](https://invisiblenetwork.ai/learn/nptel/105102001/185d1368e383) (YouTube)
2. [Fundamentals of wave propagation in periodic structures and metamaterials](https://invisiblenetwork.ai/learn/nptel/105102001/3681c4e56be2) (YouTube)
3. [Wave Dispersion in Monoatomic Chains](https://invisiblenetwork.ai/learn/nptel/105102001/7c7a8978a3a9) (YouTube)
4. [Wave dispersion in diatomic chain and mass in mass metamaterial](https://invisiblenetwork.ai/learn/nptel/105102001/19869eecee2b) (YouTube)
5. [Introduction to group velocity and phase velocity](https://invisiblenetwork.ai/learn/nptel/105102001/a606f6db1abd) (YouTube)
6. [Inertial amplifiers: Concepts of effective mass and effective stiffness](https://invisiblenetwork.ai/learn/nptel/105102001/f7cd5667fc79) (YouTube)
7. [Generalized mono-coupled systems:Negative mass and negative stiffness combinations](https://invisiblenetwork.ai/learn/nptel/105102001/789edfb4bbc2) (YouTube)
8. [Generalized mono-coupled systems:Negative mass and negative stiffness combinations (contd.)](https://invisiblenetwork.ai/learn/nptel/105102001/54948a5e133b) (YouTube)
9. [Generalized mono-coupled systems:Negative mass and negative stiffness combinations (contd.)](https://invisiblenetwork.ai/learn/nptel/105102001/22d0f5a9a12a) (YouTube)
10. [A brief introduction to Beyond Nearest Neighbours (BNNs)](https://invisiblenetwork.ai/learn/nptel/105102001/dccc82873ca3) (YouTube)
11. [Introduction to damped metamaterials-1](https://invisiblenetwork.ai/learn/nptel/105102001/0e7c2834f9fd) (YouTube)
12. [Introduction to wave propagation in damped metamaterials-2](https://invisiblenetwork.ai/learn/nptel/105102001/709047f91bd3) (YouTube)
13. [Damped matamaterial:Estimation of damping](https://invisiblenetwork.ai/learn/nptel/105102001/406edcc37201) (YouTube)
14. [Introduction to waves in continuous systems: Bar element](https://invisiblenetwork.ai/learn/nptel/105102001/4db587c60e36) (YouTube)
15. [Introduction to waves in continuous systems: Beam element](https://invisiblenetwork.ai/learn/nptel/105102001/9d5bab8c5a3c) (YouTube)
16. [Introduction to waves in continuous systems: Beam element (contd.)](https://invisiblenetwork.ai/learn/nptel/105102001/0ee4836f9a26) (YouTube)
17. [Dynamic Stiffness Matrix Formulation for Frame Elements](https://invisiblenetwork.ai/learn/nptel/105102001/fc820725da9b) (YouTube)
18. [Conical Beams](https://invisiblenetwork.ai/learn/nptel/105102001/8ff9ae2c8ed0) (YouTube)
19. [Transfer matrix formulation in continuous systems](https://invisiblenetwork.ai/learn/nptel/105102001/d0bbb601a655) (YouTube)
20. [Wave Dispersion formulation from transfer matrix](https://invisiblenetwork.ai/learn/nptel/105102001/32c9e48acb77) (YouTube)
21. [Introduction to Energy Transmission in Metamaterials](https://invisiblenetwork.ai/learn/nptel/105102001/72bcdc8571e4) (YouTube)
22. [Modulated Waves and Charasteristic Impedances in Metamaterials](https://invisiblenetwork.ai/learn/nptel/105102001/ab1de88737f6) (YouTube)
23. [Energy Accountancy in Metamaterials](https://invisiblenetwork.ai/learn/nptel/105102001/84aca1db6c60) (YouTube)
24. [Fundamentals of wave coupling and Beams with resonators](https://invisiblenetwork.ai/learn/nptel/105102001/cea5b40600ce) (YouTube)
25. [Waves in 2D lattice structures -1](https://invisiblenetwork.ai/learn/nptel/105102001/f365abf45507) (YouTube)
26. [Waves in 2D lattice structures -2](https://invisiblenetwork.ai/learn/nptel/105102001/e5227b3ccfba) (YouTube)
27. [Lecture 25](https://invisiblenetwork.ai/learn/nptel/105102001/d7f11634506a) (YouTube)
28. [Lecture 26](https://invisiblenetwork.ai/learn/nptel/105102001/ee4bfe84ba70) (YouTube)
29. [Lecture 27](https://invisiblenetwork.ai/learn/nptel/105102001/a6a885355604) (YouTube)
30. [Lecture 28](https://invisiblenetwork.ai/learn/nptel/105102001/4d4ff3cccb69) (YouTube)
31. [Lecture 29](https://invisiblenetwork.ai/learn/nptel/105102001/e86c6e4f86c0) (YouTube)