Numerical analysis of the stop band performance in finite partially treated resonant metamaterial plates

Abstract

This paper investigates the influence of partial resonant metamaterial treatments and boundary conditions on the predicted stop band performance in finite plates excited by a point-force. These finiteness effects are typically not taken into account when designing stop band performance using infinite periodic structure theory. In the first step, a finite plate in which only 24% of its surface can be treated with resonant metamaterials is defined. Stop band behaviour is analysed for different unit cell sizes that fit in the chosen treatment area. In the second step, the position of the force and treatment area in the finite plate, as well as boundary conditions, are varied to assess the influence that these parameters have on the predicted attenuation in the stop band. The attenuation in the untreated area of the plate is compared for the different models, and structural intensity analyses are performed to gain further insight into the stop band attenuation mechanisms. Design approaches are proposed to aid the design of robust resonant metamaterial systems for industrial applications.