Mr. Kumar Gourav Profile

Kumar Gourav

at Indian Institute of Technology Kanpur

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Proceedings Article | 20 April 2022 Presentation + Paper

A study on bandgap attenuation in metamaterials by varying the shape of cross-section

Kumar Gourav, Amanpreet Singh, Bishakh Bhattacharya

Proceedings Volume 12043, 120430A (2022) https://doi.org/10.1117/12.2612763

KEYWORDS: Resonators, Metamaterials, MATLAB, Aerospace engineering, Wave propagation, Vibration control, Structural design, Shape memory alloys

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Metamaterials have properties that are not usually found in conventional materials. Its unique periodic arrangement allows vibration suppression more successfully than most naturally occurring materials. In a Metamaterial beam, resonators with various designs can be attached in different configurations to obtain the bandgap according to the application requirement like vibration attenuation and waveguiding for aerospace, acoustics, or seismic isolators. This article proposes a cantilever beam with several spring-mass resonators periodically attached to it. The beam has been modelled as an Euler Bernoulli beam and is subjected to base excitation. The assumed modes method is employed to calculate the corresponding dynamic response of the structure in terms of its mode shapes. The transmissibility ratio is obtained as a function of the base excitation frequency. It is found that the transmissibility ratio is not only dependent on the excitation frequency but also the shape of the beam cross-section. Variation in the bandgap has been studied for different excitation frequencies and beam cross-sections, i.e., circular, triangular, rectangular and I-section, keeping the cross-sectional area and the mass of the beam constant. It has been observed that out of the four shapes, the I-section, rectangular and triangular or circular shapes are suitable for high, low, and intermediate frequency vibration attenuation, respectively. This study provides a basic framework to develop the metamaterial structures in an optimized manner.

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