Vibration analysis of the embedded piezoelectric polymeric nano-composite panels in the elastic substrate

In the present study the vibrations of a smart thin micro panel of polymeric nano-composite reinforced by the Single-Walled Boron-Nitride Nano-Tubes (SWBNNTs) and the matrix Poly-VinyliDene Fluoride (PVDF) on an elastic substrate is studied. Using the micromechanics method, the nano-composite structural equations are obtained for a sample volume element and by considering a unidirectional electric field and stress in the field. The stress-strain relationships that include mechanical and electric terms are obtained for the micro-tubes. The micro-panel is considered as the thin wall shell and Donnell’s non-linear theory is used for the strain-displacement relations. To obtain the equations of motion, the minimum energy method or Hamilton’s principle is used. The external work is caused by the elastic environment as well as the magnetic field energies. Given that the work has been in small micro scale the strain gradient, modified coupled stress and classic theories are used to consider the small-scale effect in the equations. The results showed Stiffness of the panel is reduced by increasing length and reducing volume fraction of BNNT and lower frequencies are obtained. Angling nanotubes is reduced panel frequency and the severity of this reduction is increased at higher volume percentages. The maximum frequency is happened in the full cylinder sector.