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An approach, based on utilizing only two sets of structural responses and the enforcement of the conditions for a unique solution, is presented for the updating of Finite Element Models. The responses required can be any two identified normal modes, any two identified complex modes, or two forced harmonic response vectors in the neighborhood of any two natural frequencies of the structure under test. The mass, stiffness, and damping matrices are interactively and simultaneously corrected in a direct noniterative procedure. A uniqueness factor is automatically computed in the procedure to indicate the correctability of the Finite Element Model under consideration. The number of measurement locations is assumed to be less than the number of degrees of freedom of the analytical model. Provisions for completing and smoothing the measured or identified responses are included to reduce the effects of measurement noise and identification error. Preliminary results on simple models are presented in support of the proposed technique.

The two problems of analytical model updating and damage detection in structures are identical in both formulation and limitations. One of the main limitations in this type of problem is the lack of sufficient information (equations) and the tendency of the mathematical models to be ill-conditioned. Multiple tests under different mass, stiffness or boundary conditions to correct an analytical model have previously been proposed to increase the amount of useful information and to improve the condition of equations. Such an approach can be costly, time consuming and prone to experimental errors.A novel approach based on single-test and multiple analytical models is presented here. The analytical model of the structure can serve as the basis for updating, in addition to several pseudo-analytical models. These pseudo-analytical models are created by randomly perturbing the original analytical model in order to maximize information and numerical stability.Examples are included in support of the proposed technique.

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