Hi all I'm a bit confused on shaft critical speed theories and I need some clarification. I'll just say what I know and point out if I am wrong in reasoning or something. I really appreciate the help. As I understand it, we are considered with the critical speed of the shaft because it is the point where an unbalance in the shaft will cause the shaft to "whirl" which damages bearings and the shaft, starts vibrations etc. because the deflection "tends to infinity". There are two methods of analysis for combined loadings Dunkerly and Rayleigh with one underestimating and the other overestimating, respectively, the first critical speed. This is because we don't know how the shaft's deflection behaves dynamically since our beam stiffness equations are based on static/quasi-static conditions. The problem I'm having trouble understanding is I never see any analysis of the components of the shaft considering the forces they transmit. For example a problem I see commonly is determining the proper diameter of a shaft for a certain critical speed safety with say a gear on the shaft. However these analyses only consider the weights of the gears and never the forces they transmit to the shaft. Obviously the gear transmits a radial force to the shaft but that is never shown to be considered in these analyses. I can't imagine that the effects can be negligible. Or simply by specifying that we stay a certain percentage below the first calculated critical speed the way we deal with that? Can someone explain? I'd appreciate it! Thank you!