Abstract
Low frequency vibrations of a thin walled functionally graded cylinder are considered within the plane strain framework. The dynamic relations in elasticity are subject to asymptotic analysis over cylinder cross section resulting in a consistent approximate equation of motion on the mid-surface. A simple explicit formula for natural frequencies emerging from the derived equation is validated by comparison with previous numerical predictions. The formula demonstrates that the ratio of the natural frequencies for functionally graded and homogeneous cylinders does not depend upon the mode number. Useful expressions for the variation of all stress components across the thickness are also obtained.