Temperature-Dependent Random Frequency of Functionally Graded Spherical shells—A PCE Approach

This paper presents the effect of temperature on random natural frequencies of spherical shells, composed of functionally graded materials (FGM) with zirconia (ceramic rich) and aluminium (metal rich). An eight noded isoperimetric quadratic element is considered for the finite element formulation. The power law is employed to construct the material modelling of Functionally Graded (FG) spherical shells. Monte Carlo Simulation (MCS) is carried out in conjunction to standard eigenvalue problems. The polynomial chaos expansion (PCE) model is constructed to reduce the computational iteration time and cost and validated it with the traditional MCS model. The statistical analyses are conducted to portray the first three random modes of frequencies. In the present analysis, the statistical results obtained are the first known results.