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

Creative Commons License

Karakaş A. İ., Daloğlu A.

Journal of Structural Engineering & Applied Mechanics, vol.2, no.4, pp.190-206, 2019 (Peer-Reviewed Journal)


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.