Abstract
The problem of crack localization has been tackled in the past by detecting frequency changes due to the application of a mass appended to the structure. However the effect of the rotary inertia of the mass on the natural frequencies of a cracked beam has not been deeply investigated. In this paper a novel explicit closed form solution of the governing equation of a beam with a concentrated mass, with rotary inertia, in the presence of multiple cracks is proposed. Furthermore, an analytical proof to show that the natural frequencies of a cracked beam with a roving body with a rotary inertia will generally change abruptly as the body passes over a crack, provided that the crack permits differential flexural rotations, is presented. Numerical results in terms of natural frequencies are provided and the procedure to exploit the occurrence of frequency shifts to detect and locate each crack is described.
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