Identification of proportional and other sorts of damping matrices using a weighted response-integral method

One of the available methods for attempting to identify a damping matrix uses a weighted matrix integral of system response functions. Validity of the method is known under a condition called 'proportional' damping but has not previously been examined For other sorts of damping. State-space approach and an associated Liapunov equation are introduced For a more general study. It emerges that all sorts of positive-definite damping matrices are in theory open to identification with a weighted matrix integral, though a formal identification result may need to be replaced with a numerical algorithm. Examples relate to simulated vibration response histories under different sorts of damping for a four-element cantilever subjected to half-sine Forcing. It is Found that error sensitivity and errors arising in extraction of impulse-response histories are apt to obscure identification: moreover that damping identifications can lack uniqueness. (C) 2001 Academic Press.