Analysis of sensitivity and robustness of forced response for nonlinear dynamic structures

An effective method is developed for calculation of the sensitivity and robustness of the forced response levels for strongly nonlinear structures. The sensitivity coefficients are determined with respect to parameters of friction contact interfaces, parameters of linear components of an assembled structure, frequency and level of excitation forces. Equations for determination of first- and second-order sensitivity coefficients of the forced response are derived analytically from a nonlinear multiharmonic equation of motion. The analytical derivation allows accurate and fast evaluation of the sensitivity coefficients. The sensitivity coefficients are calculated in frequency domain for each excitation frequency over the frequency range analysed simultaneously with the force response levels. The developed highly efficient method allows calculation of sensitivity characteristics without a noticeable increase of the computation time in addition to the time required for the forced response calculation. A measure of the forced response robustness is introduced. Sensitivity-based method for assessment of the forced response robustness for given ranges of uncertainty of structural and operating parameters is proposed. The methodology developed is illustrated on a set of problems including cases of forced response analysis for realistic strongly nonlinear gas-turbine structures.