First and second order sensitivity analysis of discontinuous parametric periodic systems

Abstract

Abstract The paper concerns sensitivity analysis of discontinuous parametric periodic systems. The eigenderivatives of monodromy matrix (Floquet transient matrix) were the first calculated. Then the first and second derivatives of multiplier, which are the complex eigenvalues of monodromy matrix, were obtained. 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. The theory has been expanded to cover a class of discontinuous parametric periodic excitations, including a situations when: the period of parametric excitation depends on the design parameters, the position of discontinuity points depends on the design parameters, and both discontinuity points and parametric constraints are a function of the design parameter. In analysis of discontinuous parametric systems the definition of distributional derivatives was applied.