Vibration analysis of boron nitride-reinforced nanocomposites embedded in elastic medium considering surface and electric field effects by using higher-order modified strain gradient theory

This paper investigates free vibration of a smart sandwich composite polymeric micro-panel blend of polyvinylidene fluoride reinforced with boron nitride nanotubes under an electric field resting on an elastic substrate using first order shear deformation theory. The distribution of nanotubes in the polymeric matrix is assumed uniformly. The Winkler springs and Pasternak shear layer are used for modeling the elastomeric substrate and the higher-order modified strain gradient theory is implemented to investigate the effects of size. First, using the microstructural modeling technique, the constitutive equations of the nanocomposite are extracted for a representative volume element, and then the stress-strain relations are obtained in terms of mechanical and electrical terms. Also, the equations of motion are derived using the Hamilton principle, and finally using the method of variational calculus and extracting the mass and stiffness matrices, the natural frequency of the micro-panel is obtained. The results of this paper show that by increasing the aspect ratio and reducing the volume fraction of nanotubes, the panel's hardness decreases and the natural frequency decreases. Further, various parameters such as the stiffness of elastic medium, the effect of electric field, different modes, aspect ratio and other factors are investigated. A comparison is also made between the classical, modified coupled stress, and higher-order modified strain gradient theories.