Parametric Instability Control of Porous Functionally Graded Beam using Piezoelectric Actuators

Abstract

This work presents the active control of parametrically excited porous functionally graded (FG) geometrically nonlinear beam integrated with extensional-mode piezoelectric actuators. The porous FG smart beam is parametrically excited by applying a compressive harmonic load along its axis. The extensional-mode piezoelectric actuators are actuated by applying an extrinsic electric field though negative velocity-feedback control strategy to resist bending deformation in beam. For the corresponding study of active vibration control, a two-dimensional incremental electro-elastic finite element model is derived. The von Karman geometric nonlinearity is accounted for large bending deformation of beam. The corresponding nonlinear finite element governing equations of motion of smart beam are solved in the frequency domain and time domain using harmonic balance method and Bathe time integration method, respectively. The results revealed that the porosity mainly reduces the critical buckling load due to the reduction in flexural rigidity. Further, it induces higher vibration amplitudes of beam or leads to the requirement of higher control electric field. In contrast, the control capability of piezoelectric actuator in controlling parametric instability increases with the porosity. Thus, extensional-mode piezoelectric actuator exhibits the adequate control capability for flexible beams compared to stiffer beams.