Analysis of Stability and Bifurcation of an Asymmetrical Rotor

The effect of shaft and disk asymmetry on the harmonic resonances of a rotor system with the in-extensional nonlinearity and large amplitude are investigated. Two rotor systems, one of which has been comprised of a symmetrical shaft and an asymmetrical disk (SA), and the other one has been comprised of an asymmetrical shaft and an asymmetrical disk (AA) are investigated. The shaft in the AA rotor has unequal mass moments of inertia and flexural rigidities in the direction of principal axes. Also, in the AA system the rigid disk is asymmetric with unequal mass moments of inertia. The equations of motion are derived by the Hamiltonian principle. The stability and bifurcations are obtained using the multiple scales method. The influences of asymmetry of shaft, asymmetry of disk, inequality between two eccentricities corresponding to the principal axes, disk position and external damping on the stability and bifurcations of SA and AA rotors are investigated. The results achieved from multiple scales method show a good agreement with those of numerical simulations.