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Based on the elasticity theory, a differential equation of forced oscillation of the blade-casing system with rub-impact excitation was deduced, and the steady analytic solution was derived. The analytic solution was verified with the FE (finite element) method, the results indicated that the eigenvalues of dynamical equation by FE method are larger than the semi-analytical method’s, while the vibration modes are identical. Due to the characteristics of rub-impact excitation between the blade and casing, it is not suitable to solve impacting vibrational response for rotating blade with the steady analytic solution. Therefore, the semi-analytical solution was adopted to solve these dynamic problems, which can get the vibration response of any position for its continuity characteristic. Then, the FE and semi-analytical method is used. The comparison of dynamical response with changing speed, rub-impact depth and the friction coefficient was investigated in details. It is found that the speed has the greater effect on the dynamical vibration response, but other parameters affect the response slightly at the same rotational speed. When the friction coefficient and rub-impact depth unchanging, with the increasing speed, the contribution of each multi-frequency component to the resonant response grows obviously, especially the high-harmonic components should be pay more attention. Blade-casing model is easy to form a new resonance system, which will appear different resonant response with the increasing friction coefficient. When the friction coefficient reaches to a certain value, the response amplitude tends to be stable.

Erratum: Research on the FE and semi-analytical solution with the blade-casing rub-impact dynamical system