Dynamic Analysis of Meta-Material Plates with Magnetostrictive Face Sheets

This study aims to control the vibrational behavior of an auxetic plate coated with magnetostrictive material. The kinematic relations of the plate, rested on a Winkler–Pasternak medium, are expressed based on the first-order shear deformation theory (FSDT). The governing equations are derived by employing the Hamilton’s principle and solved analytically by applying the Navier’s method. The effects of various parameters such as auxetic inclination angle, auxetic rib length, and feedback gain, on the control behavior of the system are monitored in detail. In order to exhibit the accuracy and validity of this study, our results are compared to those available in the literature. The results indicate that adding auxetic core to magnetostrictive plate results in increasing dimensionless natural frequency. The results obtained from this study can potentially contribute to the advancement of various applications such as the design and improvement of sensors, actuators, and vibration cancellation systems. Additionally, the obtained results could serve as a foundational basis for subsequent investigations.