Wave propagation behavior of coupled viscoelastic FG-CNTRPC micro plates subjected to electro-magnetic fields surrounded by orthotropic visco-Pasternak foundation

Wave propagation in a coupled visco-elastic micro polyvinylidene fluoride (PVDF) plate reinforced by single-walled carbon nanotubes (SWCNTs) under an electro-magnetic field will be analyzed in this study. Quasi-3D sinusoidal shear deformation theory (SSDT) of plates is presumed in order to simulate plates. The system is surrounded by orthotropic visco-Pasternak foundation. Plates are assumed to have piezoelectric property and CNTs are applied to reinforce plates in different types so micro plates are functionally graded carbon nanotube-reinforced piezoelectric composite (FG-CNTRPC); therefore, electro-magnetic field can be used as a controlling parameter for system. At first, energy equation is written according to local piezoelasticity theory and strain energy, kinetic energy and work of external forces are calculated and motion equation of system will be calculated by applying Hamilton’s principle. Finally, motion equation will be solved by using analytical solution in order to obtaining velocity of wave propagation, cut-off and escape frequency of system in different types of wave propagation in system, such as in-phase, out-of-phase and one of plate fixed. After that, the effects of magnetic field, voltage, structure damping and distributions of CNTs on velocity of system and the effects of three type of wave propagation on cut-off and escape frequency of system will be studied. Results show that the effect of out-of-phase type on phase velocity and frequency of system is more than in-phase and one of plate fixed types.