Optimal electromechanical bandgaps in piezo-embedded mechanical metamaterials

Dwivedi, A., Banerjee, A., Adhikari, S. and Bhattacharya, B. (2021) Optimal electromechanical bandgaps in piezo-embedded mechanical metamaterials. International Journal of Mechanics and Materials in Design, 17(2), pp. 419-439. (doi: 10.1007/s10999-021-09534-0)

Abstract

Elastic mechanical metamaterials are the exemplar of periodic structures. These are artificially designed structures having idiosyncratic physical properties like negative mass and negative Young’s modulus in specific frequency ranges. These extreme physical properties are due to the spatial periodicity of mechanical unit cells, which exhibit local resonance. That is why scientists are researching the dynamics of these structures for decades. This unusual dynamic behavior is frequency contingent, which modulates wave propagation through these structures. Locally resonant units in the designed metamaterial facilitate bandgap formation virtually at any frequency for wavelengths much higher than the lattice length of a unit. Here, we analyze the band structure of piezo-embedded negative mass metamaterial using the generalized Bloch theorem. For a finite number of the metamaterial units coupled equation of motion of the system is deduced, considering purely resistive and shunted inductor energy harvesting circuits. Successively, the voltage and power produced by piezoelectric material along with transmissibility of the system are computed using the backward substitution method. The addition of the piezoelectric material at the resonating unit increases the complexity of the solution. The results elucidate, the insertion of the piezoelectric material in the resonating unit provides better tunability in the band structure for simultaneous energy harvesting and vibration attenuation. Non-dimensional analysis of the system gives physical parameters that govern the formation of mechanical and electromechanical bandgaps. Optimized numerical values of these system parameters are also found for maximum first attenuation bandwidth. Thus, broader bandgap generation enhances vibration attenuation, and energy harvesting can be simultaneously available, making these structures multifunctional. This exploration can be considered as a step towards the active elastic mechanical metamaterials design.

• Item Type: Articles
• Additional Information: The authors like to acknowledge Visvesvaraya Ph.D. Scheme, Media Lab Asia, Ministry of Electronics and Information Technology, Government of India, for supporting the scholarship (MLA /ME /2015210Q) of A.D. The authors also would like to acknowledge the SPARC project (MHRD /ME /2018544) for supporting this work.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Adhikari, Professor Sondipon
• Authors: Dwivedi, A., Banerjee, A., Adhikari, S., and Bhattacharya, B.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal of Mechanics and Materials in Design
• Publisher: Springer Science and Business Media LLC
• ISSN: 1569-1713
• ISSN (Online): 1573-8841
• Published Online: 13 February 2021
• Copyright Holders: Copyright © 2021 The Authors
• First Published: First published in International Journal of Mechanics and Materials in Design 17:419-439
• Publisher Policy: Reproduced under a Creative Commons License