Detecting cracks in a longitudinally vibrating beam with dissipative boundary conditions

This paper focuses on detecting a small open crack in an axially vibrating beam with viscous boundary conditions by using non-destructive dynamical measurements. The damage is simulated by an equivalent linear elastic spring. It is shown that the measurement of the changes in a suitable pair of eigenvalues leads to the solution of the diagnostic problem, namely identification of crack location and severity. Results apply to uniform beams under various sets of boundary conditions.