Manipulating flexural waves to enhance the broadband vibration mitigation through inducing programmed disorder on smart rainbow metamaterials

The application of smart materials and metastructures has been rapidly increasing in advanced multiphysical systems because of their ability to modify mechanical responses by adding circuits in a programmable way. This paper proposes to exploit functional gradation and programmed disorder for flexural wave manipulation to enhance broadband vibration control, leading to a new application of smart metamaterials. The graded metamaterial configuration involves arranging the shunted piezoelectric patches with algorithmically obtained spatially varying parameters, resulting in wideband wave attenuation and mode trapping. The considered locally grading parameter here is the shunt resonant frequency of the unit cells, designed following the rainbow trap idea and referred to as 'rainbow' metamaterials. Two metastructures are developed in this article by tuning the shunted piezoelectric electrical circuit in single and multiple configurations, each related to the unit cell. The computationally efficient spectral element method is employed to calculate the dynamic response, and the spectral transfer matrix method is integrated therein to obtain the dispersive diagram. Subsequently, effective vibration mitigation in a wider frequency band is realized through wave manipulation based on the concept of rainbow metamaterials. To this end, we have considered a unimorph beam hosting an array of piezoelectric unit cells with single and multiple resonant shunts for obtaining the numerical results, which demonstrate that the vibration attenuation zone of the multi-resonant rainbow arrangement becomes significantly wider than the single shunt configuration. The programmed disorder in the elastic waves imposes the veering effect, which generates an interaction between two dispersion curves showing a coupling phenomenon for the waves. It involves relevant energetic exchanges between the wave modes and strongly affect the undamped forced response of the system that can influence the wave trapping generated by the proposed metamaterial. Such outcomes lead to the realization of the benefit of rainbow smart metastructures compared to conventional locally resonant metamaterials on vibration and elastic bandwidth manipulation.