Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory

In this paper, a variational approach for the wave dispersion in anisotropic doubly-curved nanoshells is presented. To study the doubly-curved nanoshell as a continuum model, a new size-dependent higher-order shear deformation theory is introduced. In order to capture the small scale effects, nonlocal strain gradient elasticity theory has been implemented. The present model incorporates two scale coefficients to examine the wave characteristics much accurately. Based on Hamilton's principle, the governing equations of the doubly-curved nanoshells are obtained. These equations are solved via analytical approach. From the best knowledge of authors, it is the first time that present formulation is used to investigate the wave dispersion in anisotropic doubly curved nanoshells. Also, it is the first time that small scale effects are considered in doubly-curved nanoshells made of anisotropic materials. Unlike the classical (scaling-free) model, the presented nonlocal strain gradient higher-order model shows a good calibration with the experimental frequencies and phase velocities. It is demonstrated that the material properties, nonlocal-strain gradient parameters and wave number have remarkable influences on wave frequencies and phase velocities. Presented results for wave dispersion can serve as benchmarks for future analysis of doubly-curved nanoshells.