Abstract: In this paper the axially symmetric, radial vibration frequency equation of multilayered cylinders made of the same materials in plain strain state is studied. It is proved in this paper that the frequency equation of several contact hollow cylinders can be replaced by the frequency equation of a single hollow cylinder, so that the solving process is greatly simplified. Some recursion formulae of Bessel functions are derived from such practical problems as well.

Key words: frequency, vibration, Bessel functions