Dynamic analysis of nanostructure in improving sports equipment assuming sinusoidal shear deformation theory and numerical solution

In this paper, dynamic response of annular nanoplates in improving sports equipment with surface effect embedded by visco Pasternak fractional foundation is studied. Size effects are evaluated by modified couple stress theory (MCST) and the surface effects are considered by the Gurtin-Murdoch theory. The structural damping effect is considered in this research using Kelvin-Voigt model. Sinusoidal shear deformation theory (SSDT) is applied for mathematical modelling of the nanostructure system. The numerical procedure of differential quadrature (DQ) is presented to determine the dynamic deflection as well as dynamic response of the annular nanoplates. The numerical results dynamic deflection of the nanostructure is considering, including material length scale parameter, spring and damper constants of visco-pasternak fractional foundation, geometrical parameters of annular nanoplates, surface stress effects.