Vibration Characteristics of Fatigue Damage of Beam-Type Structural Components

We consider free vibration of an elastic cantilever beam with a closing edge crack. The crack is simulated by an elastic pivot whose compliance is taken to be finite and is determined from the energy equivalence criterion. An algorithm has been constructed for sequential calculation of the beam vibration modes for each beam vibration cycle, whereas the number of cycles is limited. It is demonstrated that the beam vibration modes other than the initially preset one are induced during the crack opening and closing. The distinct features of such modes have been studied. We have analyzed the sensitivity of the vibration-damage characteristics which are determined from the assessment of nonlinear distortions of the displacement, acceleration, and strain waveform of the cross sections of the beam with a closing crack.