Improvement of modal scaling factors using mass additive technique

A general investigation into the improvement of modal scaling factors of an experimental modal model using additive technique is discussed. Data base required by the proposed method consists of an experimental modal model (a set of complex eigenvalues and eigenvectors) of the original structure and a corresponding set of complex eigenvalues of the mass-added structure. Three analytical methods,i.e., first order and second order perturbation methods, and local eigenvalue modification technique, are proposed to predict the improved modal scaling factors. Difficulties encountered in scaling closely spaced modes are discussed. Methods to compute the necessary rotational modal vectors at the mass additive points are also proposed to increase the accuracy of the analytical prediction

A new method to real-normalize measured complex modes

A time domain subspace iteration technique is presented to compute a set of normal modes from the measured complex modes. By using the proposed method, a large number of physical coordinates are reduced to a smaller number of model or principal coordinates. Subspace free decay time responses are computed using properly scaled complex modal vectors. Companion matrix for the general case of nonproportional damping is then derived in the selected vector subspace. Subspace normal modes are obtained through eigenvalue solution of the (M sub N) sup -1 (K sub N) matrix and transformed back to the physical coordinates to get a set of normal modes. A numerical example is presented to demonstrate the outlined theory

Spatial Information in Autonomous Modal Parameter Estimation

Recent work with autonomous modal parameter estimation has shown great promise in the quality of the modal parameter estimation results when compared to results from traditional methods by experienced users. While autonomous modal parameter estimation means slightly different things to different researchers and practitioners, for the purpose of this discussion, autonomous will require an automated procedure which sorts and processes a large number of possible modal parameter solutions to yield one consistent estimate with no user interaction after initial thresholds are chosen. In the work discussed, this final, consistent set of modal parameters is identifiable due to the combination of temporal and spatial information in a z domain state vector of relatively high order (5–10). Since this z domain state vector has both complex modal frequency and modal vector information as embedded content, sorting consistent estimates from the multitude of possible solutions is relatively trivial. Because this z domain state vector can be developed from the results of any modal parameter estimation method, possible solutions from different traditional methods can be utilized in the autonomous procedure to yield one consistent set of modal parameters