In thisJournal Bearing Rotors chapter, the period-m motionsPeriod-m motion in a 2-DOF journal bearing rotor system under external excitations is studied through the discrete mapping methodDiscrete mapping method. The stabilityStability and bifurcationsBifurcation of period-m motions will be analyzed through the eigenvalueEigenvalue analysis. The vibration of the disk of the rotor system changing with excitation frequency is investigated, and excitation effects on the journal bearing rotor system are discussed. The frequency-amplitude characteristics of periodic motions in such a 2 DOF journal bearing rotor system are presented. Numerical simulationsNumerical simulations of periodic motions are completed from mid-point integration method. The phase trajectories, displacement time-histories are provided. The harmonic amplitudes and phases varying with harmonic orders are presented from the finite Fourier seriesFinite Fourier series analysis.