Metamaterial invisibility of a corner target with proportional integral active control

Abstract

Wave invisibility in confined space has been proved practical significance in mechanical engineering and military fields. In this work, a flexural wave cloak of a corner-domain target in a metamaterial plate with proportional integral (PI) active control circuit is proposed. According to the double reflection principle and mechanical characteristic at the boundary, wave fields for a corner-domain target are defined as a collection of incident, scattering and three mirror domains. The unknown scattering mode coefficients are determined by the image method and boundary conditions. The dynamic stress concentration, scattering amplitude and scattering cross-section for the corner-domain target are obtained. The cloaking configuration is composed of multiple equally spaced concentric layers, which are filled with piezoelectric (PZT) patches. In addition, these PZT patches are connected to the active control circuit with proportional integral (PI) control module. The results indicate that the flexural wave cloak can reduce the dynamic stress concentration, scattering amplitude and scattering cross-section in corner domain. Compared to the original structure without PI active control, the effective frequency range of the active cloak can be extended by 20%.