Wave Propagation through Periodic Structures and Metamaterials

About

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)