Active vibration control of FGM plates with piezoelectric layers based on Reddy's higher-order shear deformation theory

Literature researching the active vibration control of functionally graded material (FGM) plates with piezoelectric layers using Reddy's higher-order shear deformation theory (HSDT) using any of the element-free methods does not exist. To the best of the authors’ knowledge, this paper is the first to use Reddy's HSDT with the element-free IMLS-Ritz method to investigate this problem. In this study, seven mechanical degrees of freedom (DOF) and one additional electrical DOF are considered for each node of the discretized domain. The natural frequency results of two FGM plates with top and bottom piezoelectric layers are compared with the literature in terms of various electrical and mechanical boundary conditions, volume fraction exponent (n) and dimension ratios, with obvious agreement. Furthermore, parametric studies are performed, for the first time, to study the effects of mechanical boundary conditions, n value, FGM plate thickness-to-width ratio and piezoelectric layer thickness to FGM plate thickness ratio on the natural frequency increment between open and closed circuit conditions. For the purpose of active vibration control, a constant velocity feedback approach is utilized. The effectiveness of two proposed positions, of piezoelectric sensor and actuator layers, to control the vibration of FGM plates is investigated.