Eigenvalue based inverse model of beam for structural modification and diagnostics: examples of using

Abstract

In the work, in order to solve the inverse problem, i.e. the problem of finding values of the additional quantities (mass, elasticity), the beam inverse model was proposed. Analysis of this model allows finding such a value of additional mass (elasticity) as a function of its localization so that the free vibration frequency changes to desirable value. The criteria for choice of the "proper" pair (mass -its position), including the criterion allowing changing the position of the vibration node of the second mode of the free vibrations, were given. Analysis of the influence of uncertainties in the determination of the additional quantity value and its position on the desired free vibration frequency was carried out, too. The proposed beam inverse model can be employing to identification of the beam cracks. In such a case, the input quantity is free vibration frequency measured on the damaged object. Each determined free-vibration frequency allows determining the flexibility curve for the spring modeling crack as a function of its position. The searched parameters of the crack (its depth and position) are indicated by the common point of two arbitrary curves. Accuracy of crack parameters determination depends on accuracy (uncertainty) of frequency measurement. Only some regions containing the searched crack parameters can be obtained in such a situation.