The support stiffness and connecting structure stiffness change with different assembly conditions and operating conditions. The phase and amount of rotor unbalance in different operating cycle changes due to wear of blade tip and connecting structures in different working cycles. These parameters which have significant effect on rotordynamics are “uncertain but bounded”, in another word, the distributions of the parameters are unknown, but the intervals of uncertain parameters are always got easier.

An interval analysis method, which solves the dynamic response with these uncertain parameters, has presented. Based on interval mathematics and modal superposition method, interval analysis method simplifies the uncertain parameters to interval vectors so that it can get the intervals within which the dynamic response varies when less information of structure is known. The interval analysis method is efficient under the condition that probability approach cannot work because of small samples and sparse statistics characteristics. The formulation of rotor dynamic response using interval modal superposition analysis method is formulated. A numerical example of comparison between interval analysis method and Monte Carlo method is given, and the results illustrate the interval analysis method.

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