The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells

Based on the nonlocal Love's shell theory, this paper develops an embedded magneto-electro-elastic (MEE) cylindrical nanoshell model. This model incorporates effects of the small scale parameter and thermo-electro-magnetic loadings. The surrounding elastic medium is described as the Winkler model characterized by the spring. By using this model and the Hamilton principle, the governing equations and boundary conditions are derived for free vibration of the embedded MEE cylindrical nanoshells. The Navier's method is first utilized to obtain the analytical solution for the simply supported MEE nanoshell. Then, numerical solutions for MEE nanoshells under various boundary conditions are obtained by using the differential quadrature (DQ) method. A detailed parametric study is conducted to highlight the influences of the nonlocal parameter, temperature rise, external electric potential, external magnetic potential, spring constant, radius-to-thickness ratio and length-to-radius ratio on natural frequencies of MEE nanoshells.