Enhancing bandwidth of metamaterial plate with linear and nonlinear passive absorbers

Abstract

In this work, passive vibration absorbers are used to obtain a metamaterial vibrating plate. For this purpose, a set of linear and nonlinear passive absorbers are used. The plate is modeled based on Mindlin’s theory in which the effects of rotary inertia and shear deformation are considered. The metamaterial plate is considered to be both linear and nonlinear, with a set of linear, nonlinear, and viscous absorbers (Maxwell and Maxwell–Voigt). By optimizing the absorber parameters, a noticeable reduction in the vibration amplitude of the plate is obtained, without imparting a significant mass to the original plate. The effects of mass, stiffness, damping of the absorber as well as the number of absorbers are also investigated so that the sensitivity of the behavior of the system with changing the parameters is minimized. The effect of absorbers at lower frequencies is the main focus of this work. There is more than 77% reduction in the vibration amplitude of the plate, while the total added mass is lower than 10%, which is much less than the values given in similar works. Also, the nonlinear effects of the plate have been greatly reduced and no new resonances with sufficient bandwidth have emerged, and linearization of the nonlinear plate with absorber is achieved. Finally, the performances of the used absorbers are compared.