Simultaneous mass, damping, and stiffness updating for dynamic systems
Date of Original Version
This paper presents an efficient and systematic approach to simultaneously update the mass, damping, and stiffness matrices of linear dynamic systems, given few (say two) measured complex vibration modes (complex eigenvalues and eigenvectors). The method is termed the cross-model cross-mode method because it involves solving a set of linear simultaneous equations in which each equation is formulated based on the product terms from two same/different modes associated with the mathematical and experimental models, respectively. Two numerical examples are demonstrated: a 4-degree-of-freedom mass-spring-damper system and a 30-degree-of-freedom finite element model for a cantilever beam. The numerical updating by the cross-model cross-mode method is excellent for all system matrices when the measured modes are spatially complete and noise free. The cross-model cross-mode method, together with the Guyan reduction scheme, also performs reasonably well under a spatial incompleteness situation.
Hu, Sau-Lon J., and Huajun Li. "Simultaneous mass, damping, and stiffness updating for dynamic systems." AIAA Journal 45, 10 (2007): 2529-2537. doi:10.2514/1.28605.