Nonlocal strain gradient theory for dynamical modeling of a thermo-piezo-magnetically actuated spinning inhomogeneous nanoshell

Abstract

As the main contribution, a nonlocal strain gradient theory (NSGT) is developed in conjugation with the generalized differential quadrature method (GDQM) to analyze the free vibration of a transversely graded nanoshell subjected to magnetic and thermal loads derived by using the first-order shear deformation theory (FSDT) and Hamilton’s principle. Comparisons with other common methods have shown the validity of the presented NSGT-GDQM hybrid approach. The effects of power-law exponent, nonlocal parameter, strain gradient parameter, magnetic potential, angular velocity, and temperature for both simply supported and clamped boundary conditions of a nanoshell composed of BaTiO3 and CoFe2O4 materials were investigated. Sensitivity analysis illustrates that more resolution will be available with clamped boundaries. With increasing the temperature gradient, the absolute value of the sensitivity increases and the maximum sensitivity value occurs always on the critical buckling point. Finally, comparing two studied boundary conditions revealed that if there is any temperature rise limit, the clamped boundary condition is suggested because of more sensitivity. Though the temperature gradient could be more than 400 K in the case of simply supported edges, the maximum absolute sensitivity could be obtained is about 0.12 wherein the case of clamped boundary condition it was about 0.17.