Thermomechanical active vibration control of auxetic plates with magnetostrictive layers

The current study aims to control the vibrational behavior of an auxetic plate coated with magnetostrictive material under a thermal gradient. The kinematic relations of the plate resting on a Winkler–Pasternak medium are expressed based on the first-order shear deformation theory. The governing equations are derived by employing Hamilton’s principle and solved analytically by applying 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 the present study, the results are compared to those available in the literature. The results indicate that adding an auxetic core to a magnetostrictive plate results in increasing dimensionless natural frequency. The findings of this work may be used in the development of sensors, actuators, and vibration cancellation. Also, the results might be used as a starting point for future studies.