Isogeometric timoshenko beam model and numerical verification for active vibration control of flexible rotor

A Timoshenko beam model with fewer degrees of freedom (DOFs) by isogeometric analysis method is proposed to be applied to active control of the flexible rotor and is numerically verified. This strategy solves the difficulties in the model from the standard FEM analysis, which cannot be directly employed for controller design due to the more DOFs. The isogeometric beam model with the semi-discrete form and the various boundaries are considered as the input signals in the active control for the rotor, then the singular value responses of the isogeometric beam models with more and fewer DOFs are compared, and the numerical solutions of isogeometric beam models with more and fewer DOFs and theoretic solutions both with simple supports are also compared. The rotor supported by the magnetic bearing and under the disturbances by the given distributing unbalance forces is simulated by the decentralized PD method. The results show that the singular responses of the model with fewer DOFs almost agree with those with more DOFs within the range of the sixth critical speed; the numerical solutions with more DOFs agree well the theoretic solutions within the first ten modal frequencies and the relative error of the first four modal frequencies from the model with fewer DOFs is less than 0.2%; the deviation of the steady displacement responses from the unbalance vibration between the isogeometric models with more and fewer DOFs is small and their steady response deviation can be regarded as the small disturbances with the same frequency at the working speed. The feasibility of applying directly for controller design is verified by the higher accuracy of the fewer DOFs isogeometric beam model within the low frequency range.