Active control of vibrations of piezoelectric‎ rectangular nanocomposite micro plates reinforced with graphene platelet in thermal ambient considering the structural damping

Abstract This paper investigates on the active control ‎of vibrations of rectangular nanocomposite micro plates reinforced with graphene platelet bonded with piezoelectric‎ layers in thermal environment regarding the structural damping. The micro plate is subjected to a transverse load. The thermo-mechanical features of the reinforced layers are determined employing the Halpin-Tsai micromechanical model. The first order shear deformation theory is accompanied by the modified couple stress theory to derive the motion equations of the micro plate. The Ritz technique is applied to the governing equations to discretize the equations of motion. In order to active control ‎of vibrations of the micro plate, a closed-loop PD-controller is proposed. For the sake of determination of the transient response, the Newmark- direct integration technique is applied to the discretized governing equations of motion ensuing from the Ritz technique. The present findings are validated with the available data in the literature. A parametric study is established to shed light on the impression of the material length scale parameter, the boundary condition type, the graphene platelet distribution pattern and its weight fraction, and the control gain values on the dynamic response of the micro plate when it is subjected to a pulse-uniformly distributed transverse force. The results illustrate the more effectiveness of the designed PD controller for X-GPL micro plates with four clamped boundaries especially when the size dependency is incorporated into the formulation. Moreover, the PD controller performance boosts up at higher temperatures.