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In this paper, the vibration behavior of a rotor with an asymmetric shaft subjected to unbalanced forces is analyzed theoretically. The model is a rotor composed of a rigid disk and a flexible shaft. The shaft is considered to be a beam with a rectangular cross section. The general equations of motion were first derived by considering the effect of high order large deformation in bending. In this process, a continuous shaft, gyroscopic effects, and rotor mass unbalance are taken into account to study the rotor's nonlinear vibratory behavior near the main resonances. The equations are discretized using the Rayleigh-Ritz method. The obtained equations are nonlinear coupled differential equations which are solved using the multiple-scales method. It can be concluded from the results that nonlinearity due to an asymmetric shaft severely affects the resonance behavior of the rotor. Keywords Rotor dynamics Á Nonlinear vibration Á Asymmetric shaft Á High order deformations List of symbols a 1 Amplitude at the equilibrium position (m) in x direction a 2 Amplitude at the equilibrium position (m) in z direction X Angular Velocity of the rotor (rad sec-1) x 1 , x 2 First and second critical speed of the rotor (rad sec-1) I Average area moment of inertia of shaft (m 4) c Coefficient of damping (N s m-1) R 1 Cross-sectional radius of shaft/internal radius of disk (m 2) A Cross-sectional area of shaft (m 2) q Density of material (kg m-3) r Detuning parameter (rad sec-1) u(y, t) Displacement along x-axis of rotor (m) w(y, t) Displacement along z-axis of rotor (m)

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