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A graded harmonic solid ring finite element model (FEM) is developed from the three-dimensional theory of elasticity using Fourier series expansion in circumferential direction to investigate free vibration characteristics of functionally graded (FG) thin and thick-walled cylinders parametrically. The mechanical properties of the finite length FG cylinders composed of metal (stainless steel) and ceramic (silicon nitride) are assumed to vary in radial direction according to a power law variation as a function of the volume fractions of the constituents. The frequency characteristics of the FG cylinders depending on various parameters such as circumferential harmonic number, power law exponent, thickness to radius ratio, length to radius ratio, and constituent material configuration are investigated through numerical simulations. When the graded harmonic model is compared with the previous models in the literature the agreements are found to be excellent. Also, a reduction in computational effort is provided using a smaller number of graded elements required for a fair estimation of vibrational behavior of such axisymmetric structures. As far as the numerical results are considered it is observed that thin and thick-walled cylinders behave in a different way for increasing circumferential harmonic number. The influence of the power law exponent on the frequency depends on the constituent material position and it does not affect the circumferential harmonic number at which the fundamental natural frequency occurs. As a conclusion, it can be stated that the free vibration behavior of FG cylinders can be regulated arbitrarily by altering material configuration and power law function as well as geometrical parameters.

A parametric frequency analysis for functionally graded cylinders using graded harmonic FEM