Dual functionality of vibration attenuation and energy harvesting: effect of gradation on non-linear multi-resonator metastructures

Abstract

Metastructures and phononic crystals could have several unique physical properties, such as effective negative parameters, tunable band gaps, negative refraction, and so on, which allow them to improve multi-physical performances at the materials level. Motivated by the elastic negative mass metastructures, this work reports the enhancement of bandwidth and vibration suppression while achieving better energy harvesting via non-linear attachments. We propose to consider the effect of spring softening and spring hardening simultaneously along with exploiting the coupled influence of multiple variables, such as spring stiffness, damping, number of unit cells, electro-mechanical coupling coefficient and masses. A mathematical model of the metastructure having linear spring with nonlinear attachments is developed and analyzed numerically including the effect of functional gradation. Dimensionless parametric study is performed to tune two-cell and multi-cell models to enhance vibration suppression and energy harvesting performances. In an eight-cell model, the non-linear characteristic parameter is functionally graded from softening to hardening using exponential and power law to explore the dual functionality further. It is revealed that the resonant peak can be reduced by non-linear softening characteristics. For enhanced energy harvesting, a smaller value of mass ratio is preferred, while a larger value of damping characteristic is suitable for vibration suppression. Under certain configurations, band structure of the phononic metastructure is capable of achieving absolute band gaps, resulting in frequency ranges, where waves cannot propagate. The comprehensive analysis presented here on the effect of various system parameters would lead to the design of non-linear multi-resonator metamaterials for the dual functionality of vibration attenuation and energy harvesting that can be applied in a wide range of automated systems and self-powered devices including the capabilities of real-time monitoring and active behaviour.