Damage Detection with Modal Measurements

초록

In the damage detection, the most common method relates the changes in modal characteristics (natural frequencies and mode shapes) to the modifications of the structural properties (stiffness and mass). In the modal approach, natural frequencies (eigenvalues) are preferred over mode shapes for the modal data. A minor problem occurs in that the energy equation is only a necessary condition and hence cannot provide sufficient information. Another problem comes from the fact that all degrees of freedom cannot be given in mode shapes. In structural optimization, major components are specified as desired and others are omitted. In modal measurements, a set of sensors is placed on the measurable degrees of freedom at the accessible nodes of the real structure. Therefore, primary (master) degrees of freedom are given and secondary (slave) ones are omitted in the equation formulation. The equilibrium equation of the inverse system is expressed in terms of the primary set. In the present study, the equilibrium equations of the primary degrees of freedom are employed along with the energy equation related to the frequency change. The mode shape change is expressed as the sum of the baseline mode and a complementary vector. Mathematical programming techniques are applied to minimize the deviation of the finite element model from the perturbed system. The objective function of least change tends to distribute the element changes over the entire structure. The proposed method does not involve the system transformation. The linear perturbation equation gives a good approximation, which can be improved through iterations with nonlinear perturbation equation.