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

Abstract

Metamaterials and metastructures usually exhibit some form of periodicity that is broken due to randomness in the media, affecting the vibration and elastic wave propagation performance. Disorder in the periodicity caused by the variability in properties or geometry 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, and 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 influencing wave and vibration control features. The smart unimorph meta-beam is formulated by spectral element method based on the Hamiltonian principle, and dispersion curves are estimated using the spectral transfer matrix method that relies on the Bloch-Floquet theorem. The first and second statistical moments are obtained from the stochastic simulations ( realizations) that could be realized efficiently due to the current development of spectral element approach for analysing the disordered system. Further experimental validation and exploration of shunt circuit confirms the need to include the stochastic information on the numerical model used to design the metastructure. 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. Such disorder can be exploited for enhanced functionalities of the meta-beam based on optimal RL shunt circuits for controlling structural vibration response along with wave propagation and attenuation.