Active Tunable Elastic Metasurface for Abnormal Flexural Wave Transmission

Abstract

An active elastic metasurface has more flexibility than a passively modulated elastic metasurface, owing to the manipulation of the phase gradient that can be realized without changing the geometrical configuration. In this study, a negative proportional feedback control system was employed to provide positive active control stiffness for adaptive unit cells, with the aim of achieving the active modulation of the phase gradient. The relationship between the control gain and the phase velocity of the flexural wave was derived, and the transfer coefficients and phase shifts of the flexural wave through the adaptive unit cells were resolved using the transfer matrix method. Finite element simulations for wave propagations in the adaptive unit cells were conducted, and they verified the analytic solutions. Based on this theoretical and numerical work, we designed active elastic metasurfaces with adaptive unit cells with sub-wavelength thicknesses according to the generalized Snell’s law. These metasurfaces show flexibility in achieving abnormal functions for transmitted waves, including negative refraction and wave focusing, and transforming guided waves at different operating frequencies by manipulating the control gain. Therefore, the proposed active metasurface has great potential in the fields of the tunable manipulation of elastic waves and the design of smart devices.

Keywords

• active elastic metasurface
• flexural wave controlling
• feedback control gain
• generalized Snell’s law
• piezoelectric effects