Hygro-thermo-viscoelastic wave propagation analysis of FGM nanoshells via nonlocal strain gradient fractional time-space theory

Viscoelastic behaviors of nanosize waveguides cannot be determined via simple versions of nonlocal theories if the wavelength is close to the characteristic length of the nanostructure. In such cases, a coupling between small scale and internal damping must be considered. This study is arranged to capture this important issue to provide reliable data about wave propagation responses of viscoelastic functionally graded material (FGM) nanoshells subjected to hygro-thermal loading for the first time. To do so, a tempo-spatially coupled nonlocal strain gradient viscoelasticity framework is introduced for nanoshells located in a hygro-thermally stimulated environment. First-order shear deformation theory (FSDT) is utilized and mixed with Hamilton's principle to formulate the problem for thin and moderately thick nanoshells. In the context of an analytical solution, the phase velocity of the dispersed waves is calculated. The provided data reveals that conventional size-dependent theories estimate faster damping trends for the phase velocity rather than fractional time-space theory. Also, it is demonstrated that the precision of the previously published data about viscoelastic behaviors of waves scattered in nanostructures is low in small ranges of a nonlocal parameter. This finding is attributed to the coupling between nonlocal and internal damping parameters which was not included in previous studies.