Answering two questions concerning stiffness of a Jeffcott rotor with transverse crack

We have engaged in research on Jeffcott rotor for many years. In the last few years we have engaged more deeply in the stiffness analysis of such rotor by considering the swing of disk. Our recent analysis allows us to answer two questions (the first question with confidence, the second question only tentatively): (1) the major question is why the theoretical difference between two stiffnesses, which will be defined later, reaches a peak value at a critical depth of the transverse crack; (2) the minor question is why theoretical and experimental stiffnesses differ. In the full paper, we explain in detail our recent in-depth study of the stiffnesses of Jeffcott rotor with transverse crack. The calculation of the deflections and angles of rotation of rotor with transverse crack considered and the stiffness calculation of the rotor with transverse crack are discussed. The calculations are based on fracture mechanics and strain energy density function. The effect of the depth of transverse crack on the stiffness of Jeffcott rotor, the effect of slenderness ratio on the stiffness of Jeffcott rotor, and the variations of the difference of the two stiffnesses in perpendicular directions (ξ and η) directions of the cross-section of rotor with increasing depth of transverse crack and with increasing slenderness ratio respectively are presented. We give five curves with fixed slenderness ratios of 0.01, 0.02, 0.03, 0.04 and 0.05 respectively and these five curves show that the peak values of the difference of two stiffnesses for ξ and η directions occur at critical nondimensional ratios of the depth of transverse crack to the radius of rotor vary in the small range of about 0.7 to 0.85. We can explain tentatively why theoretical and experimental stiffnesses differ.