Direct resonance response prediction of nonlinear structures: a case study on bladed disk assemblies

Ahi, Tahsin
This thesis proposes a novel method that utilizes the Response Dependent Nonlinear Mode (RDNM) concept to directly determine the resonance response of nonlinear systems without solving the system completely. The RDNM concept is introduced to decrease the nonlinear algebraic equation size in the modal superposition method by creating a new eigenvalue problem for each response level. As the response level and pattern change, the stiffness matrix of the system is adjusted accordingly. A fur ther reduction is ensured with the Dual Modal Space Method. The proposed method is evaluated on both lumped parameter and large-scale finite element models, incor porating different nonlinearities like one-dimensional dry friction model, cubic stiff ness, and one-dimensional dry friction model with normal load variation. Results demonstrate the capability of the method to predict resonance peaks accurately, with excellent agreement to frequency response solutions. Conspicuously, the proposed method reduces computational time significantly compared to the classical modal su perposition method. This thesis introduces another novel technique for utilizing complex numbered RD NMs in cyclically constrained structures. The method is demonstrated through a finite model of a large-scale cyclically symmetric shrouded blade. The proposed approach involves using complex numbered RDNMs to obtain the steady-state periodic non linear response of the shrouded blade assembly. By perturbing normal load, contact stiffness, and excitation levels, the resonance peaks are traced using complex num bered RDNMs. The results of the study demonstrate the efficacy of the proposed tech nique in capturing the nonlinear behavior of cyclically constrained structures while ensuring computational advantage.
Citation Formats
T. Ahi, “Direct resonance response prediction of nonlinear structures: a case study on bladed disk assemblies,” M.S. - Master of Science, Middle East Technical University, 2023.