Vibration control of a smart shell reinforced by graphene nanoplatelets under external load: Semi-numerical and finite element modeling

Abstract

In this article, smart control and frequency characteristics of a graphene nanoplatelets composite (GPLRC) cylindrical shell surrounded by piezoelectric layers as sensor and actuator (PLSA) are presented. The current structure is under an external load. For the semi-numerical method, the strain-stress relations can be determined through the first-order shear deformable theory (FSDT). For access to various mass densities as well as the Poisson ratio, the rule of the mixture is applied, although the modified Halpin-Tsai theory for obtaining the module of elasticity. The external voltage is applied to the sensor layer, while a Proportional-Derivative (PD) controller has been utilized for controlling the output of the sensor. The boundary conditions are derived through governing equations of the GPLRC cylindrical shell surrounded by PLSA using an energy method known as Hamilton's principle and finally are solved using a generalized differential quadrature method (GDQM). Apart from a semi-numerical solution, a finite element model was presented using the finite element package to simulate the response of the smart GPLRC cylindrical shell. The results created from a finite element simulation illustrates a close agreement with the semi-numerical method results. The outcomes show that the PD controller, viscoelastic foundation, slenderness factor (L/R), external voltage, and GPL's weight fraction have a considerable impact on the amplitude and vibration behavior of a GPLRC smart cylindrical shell. As an applicable result in related industries, the parameter and consideration of the PD controller have a positive effect on the static and dynamic behaviors of the structure subjected to an external load.