Dynamic Analysis of Functionally Graded Sandwich Doubly Curved Nanoshells Using Variable Nonlocal Elasticity Theory

Sandwich nanoshells consisting of functionally graded materials (FGMs) offer promise in aerospace, energy and biomedical applications due to their tunable properties. However, a comprehensive understanding of the vibration behavior of such shells is lacking. This work develops an efficient analytical model to study free vibration of sandwich nanoshells with three FGM configurations: FGM face-sheets and metal core (Type A), FGM face-sheets and ceramic core (Type B), and FGM core and face-sheets (Type C). A doubly curved shell geometry representing spherical, hyperbolic-parabolic and cylindrical shells in addition to flat plates is considered. Effective material properties of nanolaminates are computed using a volume fraction-based model. First-order shear deformation theory and modified nonlocal elasticity theory with variable nonlocal parameters are employed to derive the governing equations. Hamilton's principle is used to obtain the equations of motion. Navier's solution technique analytically solves the equations for simply supported boundary conditions. Accuracy is validated through comparisons with literature results. Parametric studies analyze the influence of thickness ratio, material gradation, nonlocal parameter, and shell type on frequencies. Results show that Type A configuration yields the highest frequencies. Dimensionless frequency decreases with increasing nonlocal parameter and side-to-thickness ratio. The model provides design insights into vibration behavior of such nanosandwich structures with potential applications in nanodevices and energy harvesting.