Free vibration analysis of functionally graded hemispherical shell with cut-out at apex

In this article, a finite element formulation based on First Order Shear Deformation Theory (FSDT) is used for the study of free vibration behaviour of FGM hemispherical shells with a cut-out at apex in thermal environment. A Fourier series expansion for the displacement variable in the circumferential direction is used to model the FGM hemispherical shell. The material properties of FGM hemispherical shells are functionally graded in the thickness direction according to volume fraction power law distribution. Temperature dependent material properties are considered to carry out a free vibration analysis. Numerical studies include the influence of, power law index, base to radius ratios, and different cut-out angle at apex on the magnitude of free vibration behaviour. Analysis has been carried out for hemispherical shell with clamped-clamped and clamped-free boundary conditions. It is seen that FGMs shell exhibits interesting frequency characteristics, as constitutive volume fraction varies by varying in power law index. The numerical results confirm that the vibration characteristics are significantly influenced by material composition, which in turn governs the power law index and hemispherical shell geometry.