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This study presents a nonlinear dynamic analysis of a rotor-disk-bearing system consisting of a flexible continuous rotor supported by two flexible bearings. The rotor incorporates rigid disks positioned equidistantly with zero phase difference. Both linear and nonlinear characteristics of the bearings are considered. The system's governing equations are derived using Hamilton's principle, treating the rotor as an Euler-Bernoulli beam to obtain partial differential equations. Mode shapes of a rotating beam on two springs are employed to discretize the equations via Galerkin's method, yielding ordinary differential equations. Multiple scales analysis is applied to solve the equations analytically and investigate the effects of various parameters such as linear and nonlinear bearing stiffness coefficients on stability. Frequency response curves are generated to analyze dynamic behavior. Numerical integration using the Runge-Kutta method validates the analytical solutions and excellent agreement is observed. The analyses provide insights on system behavior under flexible bearing support incorporating nonlinear dynamics.