Bandgap manipulation of single and multi-frequency smart metastructures with random impedance disorder

Abstract

Randomness in the media breaks its periodicity affecting the vibration and wave propagation performance. Such disorder caused by the variability may lead to interesting physical phenomena such as trapping and scattering waves, wave reflection, and energy localisation. While the randomness may be attributed to manufacturing irregularities and quantifying its effect is crucial for ensuring adequate performance of a range of smart systems, these effects can also be exploited for manipulating the wave properties. Here we investigate a smart metastructure in the form of a beam integrated with piezoelectric transducers coupled to a resonant shunt circuit. The piezoelectric shunt in a periodical arrangement can induce locally resonant bandgaps that can be employed in wave and vibration manipulation (and control). This paper quantifies the uncertainty associated with electrical circuit components that affect the circuit impedance. Such uncertainty essentially propagates to the beam smart metamaterial, influencing its wave and vibration control feature. Numerical results of the unimorph meta-beam with single and multi-frequency shunt configuration show that the bandgap behaviour is sensitive to the random disorder associated with circuit impedance parameters, which can, in turn, be exploited for enhanced functionalities based on optimal RL shunt circuits for controlling structural vibration response along with wave propagation and attenuation.

Vibration Characteristics of Asymmetric Flexible Cantilever Beams Connected to a Central Rigid Body

“…They explored the effects of the disorder degree on the free and forced vibrations of the disordered two-span beams. In addition, further investigation results have been published in this regard [21][22][23][24].…”