Frequency-Domain Sensitivity Analysis of Stability of Nonlinear Vibrations for High-Fidelity Models of Jointed Structures

For the analysis of essentially nonlinear vibrations, it is very important not only to determine whether the considered vibration regime is stable or unstable but also which design parameters need to be changed to make the desired stability regime and how sensitive is the stability of a chosen design of a gas-turbine structure to variation of the design parameters. In the proposed paper, an efficient method is proposed for a first time for sensitivity analysis of stability for nonlinear periodic forced response vibrations using large-scale models structures with friction, gaps, and other types of nonlinear contact interfaces. The method allows using large-scale finite element (FE) models for structural components together with detailed description of nonlinear interactions at contact interfaces. The highly accurate reduced models are applied in the assessment of the sensitivity of stability of periodic regimes. The stability sensitivity analysis is performed in frequency domain with the multiharmonic representation of the nonlinear forced response amplitudes. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic blade model with different types of nonlinearities, including friction, gaps, and cubic elastic nonlinearity.