The decoupling of damped linear systems in configuration and state spaces

✍ Scribed by Matthias Morzfeld; Fai Ma

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 142 KB
• Volume: 330
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/j.jsv.2010.09.005

✦ Synopsis

It has recently been reported that any viscously damped linear system can be decoupled in the configuration space by a real, nonlinear, time-dependent transformation. The purpose of this rapid communication is to provide a few clarifying remarks about the decoupling operation. It is shown that, for homogeneous systems, the time-dependent configuration-space decoupling transformation is real, linear and time-invariant when cast in state space. In addition, the configuration-space transformation generates a diagonalizing structure-preserving transformation. In non-homogeneous systems, both the configuration and associated state transformations are nonlinear and depend continuously on the excitation. An example is given of a linear system that can be decoupled in configuration but not in state space.