Accurate calculation of control-augmented structural eigenvalue sensitivities using reduced-order models

A method is presented for generating mode shapes for model order reduction in a way that leads to accurate calculation of eigenvalue derivatives and eigenvalues for a class of control augmented structures. The method is based on treating degrees of freedom where control forces act or masses are changed in a manner analogous to that used for boundary degrees of freedom in component mode synthesis. It is especially suited for structures controlled by a small number of actuators and/or tuned by a small number of concentrated masses whose positions are predetermined. A control augmented multispan beam with closely spaced natural frequencies is used for numerical experimentation. A comparison with reduced-order eigenvalue sensitivity calculations based on the normal modes of the structure shows that the method presented produces significant improvements in accuracy.