Examination of the fundamental frequencies of annular plates with small core

Abstract

The fundamental frequencies of vibration annular plates with small core were analyzed. The core radius at which the vibration mode switches from a non-axisymmetric mode to an axisymmetric mode was also analyzed. The influence of the boundary conditions and the Poisson ratio on the transition core radius, b, was also discussed. Asymptotic expansion on the the exact characteristic equations delineates the singular rise of the fundamental frequency when the core size was close to zero. For b=0, the fundamental frequency was zero for clamped-free (CF) and supported- free (SF) plates.