Abstract
In the present study, the effect of a crack on the dynamic stability of a free–free Timoshenko beam is investigated when it is subjected to a constant or a pulsating follower force. A crack, one of the structural damages, results in a change of transverse vibration frequencies and mode shapes. In addition, the crack may change the stability characteristics of the beam. A mathematical model for the crack is introduced in the form of the bending and shear compliance of equivalent incremental strain energy. To obtain numerical results, the finite element method and the method of multiple scales are applied in this work. As a conclusion, the effect of the crack location and depth on the stability characteristics of the system is illustrated.
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