Free vibration of piezoelectric boron nitride nanotube-based composite cylindrical micropanel embedded in an elastic medium subjected to electric potential via modified strain gradient theory

Abstract

This paper deals with the free vibration analysis of a smart polymeric composite sandwich micropanel made of polyvinylidene fluoride reinforced by single-walled boron nitride nanotubes resting on an elastic substrate under an electric field. The analysis procedure is based on the first-order shear deformation theory and modified strain gradient theory to investigate the size-dependent effect. The nanotubes are assumed to be uniformly distributed within the polymeric matrix. The elastomeric substrate is modeled using Winkler springs and a Pasternak shear layer. First, the constitutive equations of the nanocomposite are derived for a unit cell using a micro-electromechanics modeling technique, and the stress–strain relations are subsequently obtained with regard to mechanical and electrical terms. The equations of motion of the micropanel are obtained based on the Hamilton principle. Finally, the natural frequencies of the micropanel are obtained by extracting the mass and stiffness matrices through the method of variational calculus. A parametric study is further performed to investigate the effect of various parameters such as the stiffness of the elastic medium, the effect of electric field, different modes of vibration, aspect ratio, and so on. It is observed that the panel’s stiffness and, consequently, the natural frequency decrease as the aspect ratio increases and the nanotube volume fraction reduces. A comparison is also conducted with the classical continuum theory and modified coupled stress theory.