Dynamic Flexibility Method for Extracting Constrained Structural Modes from Free Test Data

Abstract

A method for extracting constrained modes from free-boundary modal test data is developed as an alternate approach when the constrained modal survey proves dife cult. The transformation relationship between the modes ofafree‐freestructureand thoseofa corresponding constrained structureisdescribed,and a nonlinearcharacteristic equation is derived. Then an eigenvalue shifting technique, which can also improve computational efe ciency, is employed to avoid the singularity of the stiffness matrix of free structures. The method utilizes a subset of measurable lower-order free modes plus the effects of neglected higher-order modes on the dynamic e exibility matrix. However, theanalytical or measured higher-order modesof a freestructure are unknown ordife cult to obtain, and so the contribution of the higher-order modes to the dynamic e exibility matrix is expanded as a power series. The constrained modes are obtained by solving the nonlinear characteristic equation. It will be seen that this method is a typical substitute for the procedures based on experimental and theoretical modeling. Numerical simulation demonstrates that the method can converge quickly and has satisfactory precision.