Solving Fundamental Partial Differential Equation for Mistuned Bladed Disk Vibration

In this study, a new approach is developed to solve the mistuned bladed disk partial differential equation (PDE) with arbitrary spatial nonuniformities, and obtain natural frequencies, mode shapes, and steady-state response. The method is based on the novel approach developed by the author to compute natural frequencies and mode shapes of a one-dimensional continuous structure with arbitrary nonuniformities and discontinuities. This method is based on the state transition matrix and has also been applied to a circular membrane with radial non-uniformities, and resulting mode shapes are used to develop a reduced-order model for a circular membrane with both radial and circumferential nonuniformities.