Controlling the effective bending stiffness via out-of-plane rotational resonances in elastic metamaterial thin plates

Abstract

In this work, we investigate the effective parameters of elastic metamaterial thin plates. We find that the out-of-plane rotational resonances can lead to a resonant behavior in the effective bending stiffness of metamaterial thin plates, which provides a route to tune the effective bending stiffness independently, from positive to negative values, and even infinity. By using resonant frequency analysis for metamaterial plates with different sizes, we have verified the resonant nature of the effective bending stiffness. Moreover, by designing a new type of elastic metamaterial plate with enhanced moment of inertia, we demonstrate a convenient way to tune the frequency regime of negative bending stiffness to overlap with that of negative mass density, and thus realize a band of negative group velocity. With the effective mass density and bending stiffness being independently tunable, the resonance properties of the elastic metamaterial thin plate can be engineered efficiently. Our work demonstrates a unique approach for manipulating flexural waves in elastic metamaterial thin plates.

Keywords

• bending stiffness
• elastic metamaterial
• thin plate
• rotational resonance