Sensitivity Analysis of Modal Parameter Based on Simple Scaling for Asymmetric Damped System

PurposeIn fact, the diagonal elements of the modal matrix are read in the form of the normalization constants, which is the case in both experimental modal analysis and analytical modal analysis. A desired performance in both above fields will require simple scaling of the mode shapes. In this study, a method to calculate the sensitivities of modal parameters based on a simple scaling scheme for asymmetric damped system is presented to meet this requirement.MethodsThe normalization constants are designed to be open. Also, only one equation of normalization condition is adopted to establish a series of comparatively simple formulas for the proposed algorithm.Results The influences of normalization constants on the sensitivity analysis and its numerical aspects are further investigated. A numerical example is presented to demonstrate the accuracy and good applicability of the proposed algorithm.ConclusionsThe major advantage of the proposed algorithm lies in the fact that, without the need for normalizing the left eigenvector or searching for its sensitivity, not only can computation be reduced, but also potential numerical problems can be avoided.