Modal analysis of rotating shafts: A body-fixed axis formulation approach

Abstract A spinning Timoshenko beam subjected to a constant moving load is analyzed using a modal expansion technique. The formulation is based on a body-fixed axis reference system, and thus should be applicable to handle any general cross-sections. Using this alternative approach, dynamic quantities such as natural frequencies, mode shapes and system responses are easily computable. It is shown that simply supported spinning Timoshenko beams posses two pairs of natural frequencies corresponding to each mode shape. Through appropriate simplifications, the coupled eighth order differential equations governing the problem are degenerated into a set of uncoupled fourth order equations. With this simplified theory, closed form expressions for natural frequencies and system transient response are derived. However, one pair of the natural frequencies is lost in the process, but this is acceptable as the frequencies of this pair are much higher than those of the retained pair. In addition, a linearized approximation of the natural frequency, similar to the one given for Euler-Bernoulli beams, is also proposed for a Timoshenko shaft. Numerical simulations are performed to demonstrate the characteristics of the response.