Coupled longitudinal and bending forced vibration of Timoshenko cantilever beam with a closing crack

The paper presents the method of modelling of the coupled longitudinal and bending forced vibrations of the Timoshenko cantilever beam with a transverse, one-edge, non-propagating, closing crack. Two models of closing crack are examined in the paper. The beam is modelled by the finite element method. The equation of motion is formulated using the harmonic balance method. The influence of various parameters (crack location and its depth, axial force frequency, closing crack model etc.) upon the steady state response of the beam free end is analyzed. The possibility of crack detection based on the analysis of higher harmonics variations in the frequency spectrum is examined.