International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

The linear theory including the effects of bending-torsion coupling and rotatory inertia is used to derive the equations of motion for a space beam with variable curvature. The governing differential equations of motion are derived based on Euler-Bernoulli beam theory via Hamilton’s principle. The full, coupled system of governing partial differential equations has a total order of 12.

The natural frequencies and mode shapes of an Euler-Bernoulli beam with a rectangular cross- section, which has a surface crack, is investigated. The crack is modeled as a change (sudden or gradual) in the cross-section of the beam, and the perturbation approach is used assuming that the crack is much smaller than the beam cross section. Computations of natural frequencies and mode shapes were carried out for four different crack shapes with rectangular, triangular and parabolic profiles when viewed through the side of the beam. The results are listed in non-dimensional form for various values of the parameters characterizing the crack.