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 `proportionalʹ 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.