Analytical and mesh-free approaches to dynamic analysis and active control of smart FGP-GPLRC beam

Abstract

This paper aims to perform the dynamic analysis and active control of a functionally graded porous beam reinforced with graphene platelets (GPLs) and embedded in piezoelectric layers (smart FGP-GPLRC beam). Two types of porosity distribution combined with three dispersions of GPL pattern for the FGP-GPLRC beam are considered. The Halpin–Tsai model is used for estimating the effective elastic modulus of the FGP-GPLRC beam. The linear electric potential field through the thickness of each piezoelectric layer is assumed. Energy principles are applied to establish the equations of motion, which are then solved by two approaches. The first one is an analytical method with the Navier technique and the second one is a mesh-free method based on the polynomial basis in conjunction with the C1 Hermite interpolation technique. Newmark's integration algorithm with constant average acceleration is employed to determine the time-dependent response. The velocity feedback control algorithm is utilized to actively control the vibration response of the smart FGP-GPLRC beam. The convergence of mesh-free analysis is performed through a numerical test. Various comparative examples are carried out rigorously to verify the accuracy of the current study. Influences of porosity and GPL parameters, open- and closed-circuit states on the natural frequency, and forced vibration of the smart beam are investigated via numerical examples. In addition, the study also examines the effects of velocity feedback control gain on vibration suppression and the prevention of the beat and resonance problems occurring in the smart beam. Finally, the solution of using a collocated piezoelectric sensor/actuator pair on the same side of the FGP-GPLRC beam to guarantee the stability of the vibration control with the stretching-bending coupling effect is illustrated.