In this article, the free vibration behavior of a functionally graded (FG) size-dependent microshell surrounded by viscoelastic foundation subjected to various thermal loading conditions is analytically studied. The material properties of the cylindrical FG microshell are supposed to be temperature dependent and vary continuously along the thickness direction according to the modied rule of mixtures. The size-dependent FG microshell is analyzed based on the modied couple stress theory. The analytical modeling is developed using the rst-order shear deformation theory and the equations of motion are derived by the principle of minimum total potential energy. Then the governing equations for the free vibration behavior of a simply supported FG cylindrical microshell subjected to thermal loading are solved using the Navier procedure. The eects of some important parameters, such as material length scale parameter, stiness and damping of the visco-Pasternak foundation, temperature changes, axial and circumferential wave number, and length of the microshell on the natural frequency are investigated and discussed.
