In-plane vibration of annular disks using finite elements

The axisymmetric and asymmetric in-plane, free vibration of annular disks using the finite element method is discussed. The in-plane behavior is analyzed by annular ring segments using a Fourier series approach to model the problem asymmetries. Using displacement functions which are exact solutions to the in-plane static problem, the stiffness matrices corresponding to the 0th, 1st and nth harmonics are derived. By assuming that the static displacement functions closely represent the vibration modes, the mass matrices for various harmonics are also derived. These matrices can be readily coded into any special or general purpose structural analysis computer programs. Results of example problems are compared with exact solutions