Eigen problem Sensitivity Analysis of Continuous Parametric Periodic Systems

Abstract

Abstract The paper concerns sensitivity analysis of the complex eigensolutions of monodromy matrix (Floquet transient matrix) for continuous parametric periodic systems. The first and the second derivatives of monodromy matrix and its multipliers which are the complex eigenvalues of monodromy matrix have been calculated. The method’s innovation is the idea to achieve the sensitivity equation by evaluating the derivative of the parametric equation of motion. Then, by solving the sensitivity equation obtained in this way, to evaluate the first and second derivative of monodromy matrix and finally the first and second derivatives of multipliers. Furthermore, the sensitivity analysis method was improved and generalized to allow to correctly determine the eigenderivatives also with respect to those system parameters, on which the parametric excitation period depends. In particular, it becomes possible to use the parametric excitation period as a design parameter.