For rotating disks, the effect of axisymmetric runout is of interest. This study examines the frequency characteristics of thin rotating discs subjected to axisymmetric non-flatness. The equations of motion used are based on Von Karman’s plate theory. First, the eigenfunctions of the stationary disk problem corresponding to the stress function and transverse displacement are found. These eigenfunctions produce an equation that can be used in the Gelrkin’s method. The initial nonflatness is assumed to be a linear combination of the eigenfunctions of the transverse displacement of the stationary disk problem. Since the initial non-flatness is assumed to be axisymmetric, only eigenfunctions with no nodal diameters are considered to approximate the initial runout. It is supposed that the disk bending deflection is small compared to disk thickness, so we can ignore the second-order terms in the governing equations corresponding to transverse displacement and stress function. After simplifying and discretizing the governing equations of motion, we can obtain a set of coupled equations of motion which takes the effect of initial axisymmetric runout into account. These equations are then used to study the effect of initial runout on the frequency response of the stationary disk. It is found that the initial runout increases the frequencies of the oscillations of a stationary disk. In the next step, we study the effect of initial non-flatness on the critical speed behavior of a spinning disk.

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