Periodic Stability and Sensitivity Analysis of Rotating Machinery

This work presents the evaluation of periodic stability of rotating machinery and its sensitivity analysis. The stability criterion is based on the characteristic exponents or more generally the eigenvalues of the monodromy matrix of the periodic system following Floquet's Theory. Parametric sensitivity of the stability is formulated to provide a methodology for robustness in rotating machinery analysis and design. The problem is formulated for a generic rotating dynamical system having periodic coefficients and demonstrated on a helicopter blade in forward flight and on a cracked rotating shaft.