This book presents a systematic and rigorous treatment of wave propagation in periodic structures, with a particular focus on mechanical and acoustic metamaterials. It bridges fundamental concepts and advanced topics, offering a unified framework to analyze discrete and continuous periodic systems.
Metamaterials are artificial, engineered materials designed to manipulate wave propagation in ways not possible with conventional materials. An Introduction to Waves in Mechanical Periodic Structures and Metamaterials presents a systematic and rigorous treatment of wave propagation in periodic structures, with a particular focus on mechanical and acoustic metamaterials. The book bridges fundamental concepts and advanced topics, offering a unified framework to analyze discrete and continuous periodic systems. Key topics include:
- Comprehensive mathematical formulation of wave propagation in solids and periodic structures
- In-depth discussion on bandgap formation through Bragg scattering, local resonance, and inertial amplification
- Coverage of advanced concepts such as meta-damping, non-reciprocity, active control, and nonlinear metamaterials
- Unique focus on damping evaluation in metamaterials, critical for shock resistance and transient dynamic applications
This book serves as an accessible yet rigorous resource for senior undergraduate and graduate students in structural engineering, mechanical engineering, applied physics, and materials science, as well as for researchers seeking to deepen their understanding of wave mechanics in metamaterials.
Part I. Foundational Aspects of Waves in Metamaterials.
1. Introduction.
2. Waves in Discrete 1D Periodic Structures.
3. Damping in 1D Discrete
Medium.
4. Dynamic Stiffness Matrix for 1D Continuum.
5. Band Structure in 1D
Continuum: Transfer Matrix Approach. Part II. Advanced Topics.
6. Energy
Transportation in Wave Propagation.
7. Two-Dimensional Wave Propagation.
8.
Active Feedback-Controlled Metamaterial.
9. Nonreciprocity in Wave
Propagation.
10. Nonlinear Metamaterial.
Arnab Banerjee is Associate Professor in the Civil and Environmental Engineering Department, Indian Institute of Technology Delhi. His research focuses on structural dynamics, wave mechanics, and metamaterials for vibration control in infrastructure and renewable energy systems. He has pioneered work in subwavelength attenuation, active control of ultra-wide bandgaps, meta-dissipation, and non-reciprocal metamaterials. Dr. Banerjee's innovations have led to multiple patents and extensive publications, earning him several national and international recognitions, including induction asYoung Associate in INAE, Early Career Research Awart from IIT Delhi, Inspire faculty award from DST India, and the Newton International Postdoctoral Fellowship from the Royal Society London.
Kamal Krishna Bera is Assistant Professor in the Civil Engineering Department, National Institute of Technology Tiruchirappalli. His expertise spans structural dynamics, vibration control, and wind-induced instabilities,including offshore wind turbines and metamaterial-based isolation. He has pioneered work in active control of ultra-wide bandgaps, meta dissipation, and non-reciprocal metamaterials. He actively collaborates on research in periodic structures and has published widely in leading journals. Dr. Bera combines academic research with practical industry experience in structural engineering.
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