In this treatise, for the first time, the vibration behavior of truncated conical sandwich shells reinforced with graphene platelets and having a porous core and face sheets, which are reinforced with rings on the outer surfaces and are under point supports at the boundaries, has been investigated. In this regard, the free and forced vibration of such shells have been studied. Truncated conical shells are one of the well-known important structural components in the many engineering branches such as power plants, petrochemical, aerospace, marine and so on. The demands of modern industries for advanced materials with superior thermo-mechanical properties such as high strength- and stiffness-to-weight ratios, high wear resistance, high thermal and electrical conductivity over the conventional materials encouraged scientists to research and develop new high-performance materials. In recent years, composites with carbonaceous nanofillers reinforcement have been widely used in various engineering sectors due to very favorable thermal, electrical and mechanical properties. So, this kind of nanofillers have emerged as ultra-lightweight reinforcement materials together with extremely high strength- and stiffness-to-weight ratios, high thermal and electrical conductivity, and high wear resistance. On the other hand, the progress in technology provides tools and capabilities for manufacturing advanced composite materials with nanofiller reinforcements. Consequently, the use of these advanced materials is becoming increasingly popular to develop complicated high-performance composite structures. On the other hand, reinforcing the thin-walled shell composite structures with the circumferential stiffeners, increases their load carrying capacity significantly and also, reduces the amount of consumable materials required for their manufacturing. During the manufacturing process, the void spaces (or the so-called porosities) in a material can be occurred unintentionally or in a cont