Analytical modeling of wave propagation in viscoelastic functionally graded carbon nanotubes reinforced piezoelectric microplate under electro-magnetic field

Wave propagation analysis of a functionally graded carbon nanotubes reinforced piezoelectric composite (FG-CNTRPC) microplate is the major main of the present research. In order to present a realistic model, the material properties of the system are assumed viscoelastic and the Kelvin–Voigt model is applied. The viscoelastic FG-CNTRPC microplate is subjected to longitudinal magnetic and three-dimensional electric fields. The distribution of carbon nanotubes in FG-CNTRPC microplate is supposed as uniform distribution and surrounding circumference is simulated as Visco-Pasternak foundation. The original formulation of the quasi-three-dimensional sinusoidal shear deformation plate theory is here extended to the wave propagation analysis and the size effects are considered based on Eringen’s nonlocal theory. In order to calculate the dimensionless frequency, cut-off and escape frequencies analytical solution is applied. In this article, the influences of the volume fraction of carbon nanotubes, electro-magnetic fields and elastic medium on the dimensionless frequency of viscoelastic FG-CNTRPC microplate are investigated. Furthermore, the effect of small-scale parameter on the cut-off and escape frequencies of the system will be studied. Results demonstrate that the dimensionless cut-off and escape frequencies decrease with increasing the magnitude of small-scale parameter. In addition, the imposed magnetic field and external voltage are significant parameters for controlling wave propagation of the viscoelastic FG-CNTRPC microplate. Results of this investigation can be helpful for the study and design of composite systems based on smart control and sensor applications.