Frequency response functions and finite element equations with rigid-body constraints, and their application in model updating

A method is proposed for the replacement of unknown stiffnesses with rigid connections in two systems of equations from a finite element model and from measured frequency response functions. The frequency responses can be determined from standard modal tests and no special forcing arrangements or physical constraints are needed. The only use of constraints is in the mathematics where the physical behaviour of a constrained system is inferred from the unconstrained measurements, and predictions are obtained from constrained finite element equations. Since stiffnesses which are replaced by rigid connections cannot experience any elastic strain they can have no effect on the inferred measurements from an elastic structure, or on the constrained predictions. The method can be used to determine erroneous connections in a finite element model or to locate discrete (and unmodelled) nonlinearities. Simulated examples are used to illustrate the application of the technique.