Saeidreza Mohebpour

The vibrational behavior of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) toroidal panels with elastically restrained against rotation edges is investigated. The first-order shear deformation theory (FSDT) of shells together with the finite element method (FEM) is employed to develop a general formulation and solution procedure. Nine-noded isoparametric shell elements with five degrees of freedom per node are used to discretize the spatial domain. After validating the approach, the influences of different distribution patterns of graphene platelets (GPLs) through the panel thickness, the geometrical parameters, and the elastic coefficients of the rotational springs are studied. It is shown that among the multilayer FG-GPLRC toroidal panels with different GPLs distribution patterns, the toroidal panels with X-type pattern have the highest frequency values whereas the minimum values belong to the shells with O-type and -type for the first and second frequency parameters, respectively. Also, the numerical results reveal that by increasing the GPLs volume fraction and the elastic coefficients of rotational springs, the frequency parameters increase, and these parameters have considerable effects on the frequency parameters. Also, the mode shapes of multilayer FGGPLRC toroidal panels for different GPLs distribution patterns are depicted.