An analytical approach for free vibration analysis of Euler-Bernoulli stepped beams with axial-bending coupling effect

Free vibration of eccentrically stepped beams with one step change in cross-section is considered. It is assumed that the longitudinal symmetry axes of the beam segments are translationally shifted along the vertical direction with respect to each other. The effect of that arrangement of the segments on the coupling of axial and bending vibrations of the stepped beam is analyzed. The beam segments are modeled in the frame of the Euler-Bernoulli theory of elastic beams. Two numerical examples are presented.