Open AccessEigen problem Sensitivity Analysis of Continuous Parametric Periodic Systems
Author(s) -
Zbigniew Wójcicki
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/661/1/012042
Subject(s) - monodromy matrix , sensitivity (control systems) , eigenvalues and eigenvectors , parametric statistics , monodromy , matrix (chemical analysis) , mathematics , floquet theory , mathematical analysis , derivative (finance) , physics , pure mathematics , statistics , nonlinear system , materials science , quantum mechanics , engineering , economics , composite material , electronic engineering , financial economics
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.