On the poroelastic vibrations of lightweight FGSP doubly-curved shells integrated with GNPs-reinforced composite coatings in thermal atmospheres

Porous and nanocomposite materials are widely used in various engineering structures due to their exceptional thermos-mechanical properties. In this work, the poro-thermoelastic frequency analysis of three-layer functionally graded saturated porous (FGSP) lightweight shells covered with two graphene nanoplatelets (GNPs)-reinforced composite surfaces is explored. Both the volume fraction and the diffusion types of GNPs reinforcement in the patches are investigated and moreover, the effect of pressure exerted by the fluids in the openings is considered and the different pore arrangements are compared. Based on the first-order shear deformation theory (FSDT) combined with Hamilton's principle, the equations of motion are derived and then solved analytically. After confirming the accuracy of the results, the frequencies are presented for different types of shells, including cylindrical, spherical, and doubly-curved shells. These types of shells are widely used in various industries, so the results of this work can be useful for these industries. In addition, this is the first comprehensive frequency analysis for different types of shells, and the results can serve as a benchmark for future studies.