Asymmetric vibration and stability of circular plates

The asymmetric vibration and stability of circular and annular plates using the finite element method is discussed. The plate bending model consists of one-dimensional circular and annular ring segments using a Fourier series approach to model the problem asymmetries. Using displacement functions which are the exact solutions of the static plate bending equation, the stiffness coefficients corresponding to the 1st and nth harmonics are used in closed form. By assuming that the static displacement function closely represents the vibration and stability modes, the mass and stability coefficient matrices for an annular and circular element are also constructed for the 1st and nth harmonics. Several numerical examples are presented to demonstrate the efficiency and accuracy of the finite element model with that of classical methods.