Electro-magneto temperature-dependent vibration analysis of functionally graded-carbon nanotube-reinforced piezoelectric Mindlin cylindrical shells resting on a temperature-dependent,orthotropic elastic medium

Vibration smart control analysis of a temperature-dependent functionally graded-carbon nanotube-reinforced piezoelectric cylindrical shell embedded in an orthotropic elastic medium is investigated. The mixture law is used for obtaining the material properties of the structure. The structure is subjected to a 2D magnetic field. Considering the first-order shear deformation theory, the motion equations are obtained. Based on an analytical method and differential quadrature method, the frequency is calculated. The effects of applied voltage, magnetic field, volume percent, and distribution type of carbon nanotubes, temperature, orthotropic elastic medium, and length to radius ratio of the shell are shown on system frequency.