A Method for Determining Model-Structure Errors and for Locating Damage in Vibrating Systems

JE Mottershead (Liverpool University), MI Friswell, University of Wales Swansea, C Mares (Liverpool University)

Meccanica, Vol. 34, No. 3, August 1999, pp. 153-166


A method is proposed for the determination of natural frequencies and mode shapes of a system which is constrained so that unknown stiffnesses are replaced with rigid connections. The constraint is not imposed physically but only in the mathematics so that the behaviour of the constrained system is inferred from the unconstrained measurements, and predictions are obtained from constrained finite element equations. Since stiffnesses which are made rigid cannot experience any elastic strain they can have no effect on the inferred measurements. A procedure for comparing the inferred measurements with similarly constrained finite element predictions can be used to determine model-structure errors. Damage, such as a crack in a beam can be located by comparing the inferred measurements from the structure in undamaged and current states. It is demonstrated how unmeasured rotations may be constrained by using rigid-body modes and a reduction/expansion transformation from a finite element model.

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Link to paper using doi:10.1023/A:1004684417925

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