Free-vibration response of functionally graded porous shell structures in thermal environments with temperature-dependent material properties

This article deals with free vibration response of functionally graded cylindrical and spherical porous shells in thermal environments with temperature-dependent material properties. The effective material properties are determined via the rule of mixture with porosity phases. The equation of motion is developed based on a curved 8-node degenerated shell element formulation using the principle of virtual work. Two different material mixtures are considered, the first one is zirconium oxide and titanium alloy referred to as ZrO2/Ti-6AL-4V, and the second one is silicon nitride and stainless steel referred to as Si3N4/SUS304. The influence of material constituents, power-law indexes, boundary conditions, radius to thickness ratio, porosity parameter, and temperature gradient on the natural frequencies is studied in detail. It is found that the porosity of the constituent material has a significant consequence on the vibration response of FGM shells, especially in high temperatures.