Dynamic analysis and active control of smart doubly curved FGM panels

In this paper, active control and dynamic analysis of shallow doubly curved functionally graded material (FGM) panels integrated with sensor/actuator piezoelectric layers are presented, analytically. Properties of the FGM panel are dictated using a simple power law model across the thickness. Based on the modified Sander’s shell theory combined with first order shear deformation theory, total potential energy of the system is derived. Five mechanical equilibrium equations and two electrical equations are established as the governing equations. The classical negative velocity feedback controller rule is implemented to suppress the vibration response of the panel. For both the active and passive cases, established equations are reduced into new five equations in terms of displacements and rotations. Employing the combined analytical Fourier–Laplace transformation, consistent with the panels with movable simply-supported edges, an accurate closed-form solution is resulted for response of the panel in both active and passive cases in real time domain.