## 1 Introduction  
For the purpose of searching for optimal design parameters for rotating machinery, investigations of the dynamic characteristics of the system, such as stability analysis [1, 2], reliability analysis [3] and optimal design analysis [4] based on specific criteria, have been performed by many scholars. Typically, a sensitivity analysis is also suggested when researching the dynamic characteristics of a system. Sensitivity analysis can provide quantitative information about to what extent does the responses of rotating system change when the design parameters varies from a base case, thus dominant impact factors can be found based on a restricted number of cases rather than enormous amount of data. In general, there are two different kinds of methods measuring sensitivities of the investigated system, i.e., local and global sensitivity analysis [5, 6]. Local sensitivity analysis, which is in the topic of this paper, is performed by investigating the influence of slight deviation from nominal values of different design parameters on the output parameters, i.e., the maximum amplitudes of certain degrees of freedom. Many scholars have contributed to the applications of sensitivity analysis to specific domains. [PERSON] [7] et al. proposed a method to assess the extent of rotor failure and investigated the frequency reliability sensitivity with respect to several stochastic parameters. [PERSON] and [PERSON] [8] presented a structural sensitivity analysis approach based on moment and compared the results with those computed by a conventional Monte Carlo method. [PERSON] [9] et al. combined sensitivity analysis with Monte Carlo methods by introducing a supplementary procedure. [PERSON] [10; 11] et al. investigated the sensitivity of the steady response of bladder disk assemblies with respect to parameters of nonlinear friction contact interfaces. [PERSON] [12] et al. proposed a new sensitivity analysis method for a rotor supported by two bearings. [PERSON] and [PERSON] [13] studied the sensitivity of large turbine shaft system with respect to shaft unbalance. [PERSON] [14] et al. applied sensitivity analysis to investigate the influence of the mass and the offset of disk on rotors. And results have revealed that the offset of disk influence the critical speed in a significant way. [PERSON] [15] et al. carried out a sensitivity analysis on solid rotor induction machines. [PERSON] [16] et al. investigated the load change sensitivities of a multi-support system utilizing virtual displacement principle. Based on the model they proposed, the influence of load variation on dynamic characteristics and sensitivities of a multi-support structure is researched. [PERSON] [17] et al. carried out sensitivity analysis and uncertainty qualification for a coaxial rotor system, where the sensitivities of hub loads with respect to ambient drift speed, rotor angular speed and center of gravity location on the blade are investigated. Furthermore, rubbing phenomenon is expected when the clearance between rotor and stator becomes so small that friction and collision happens at interfaces. It makes the response of rotor strongly nonlinear and is sensitive to parameters of friction interfaces. Investigations of dynamic analysis for rotors with rub-impact have been performed by many researchers. [PERSON] and [PERSON] [18] found that the rub-impact becomes more severe with increase of imbalance of rotor. [PERSON] [19] et al. presented that the increase of excitation force would result in the transformation of contact status, i.e., from partial rubbing to full rubbing. [PERSON] and [PERSON] [20] investigated the vibration characteristics of a rotor with rub-impact resulting from initial perturbations. [PERSON] [21] et al. utilized full spectrum analysis to investigate the vibration characteristics of a cracked rotor rubbing with stators. The research done by [PERSON] [22] et al. showed that a reduction in structural damping will result in a periodic response of the rotor subjected to rub-impact to become non-periodic.