Vibration analysis of sandwich beam with honeycomb core and piezoelectric facesheets affected by PD controller

Free vibration analysis of a sandwich beam with honeycomb core and piezoelectric face sheets, which is rested on the viscoelastic foundation is investigated. The thermal environment and the electric field are applied to this structure. Also, it is affected by the proportional-derivative (PD) controller. The amount of gain in this controller can affects the vibration frequency. The displacement components are expressed by improved high-order sandwich panel theory (IHSAPT) that considers continuity conditions for transverse shear stress at the interfaces and the zero transverse shear stresses conditions on the upper and lower surfaces of the beam and core flexibility. The motion equations are derived and solved by Hamilton's principle and Navier's method, respectively. This paper examines the effects of various parameters, such as the internal aspect ratio and the cell angle/thickness of the honeycomb core, temperature variations, viscoelastic environment, electric load, and control gain on its natural frequencies. The results show when the honeycomb core's to face sheet's thickness ratio increases, the beam dimensionless frequency increases, too. Also, by increasing the internal aspect ratio of honeycomb core, the frequency of sandwich beam decreases. The results of this study can be used to vibration control in aerospace engineering and constructions.