One nonlinear partial differential equation of cracked beam flexural vibrations is derived. Crack function and displacement function are used to describe the perturbation of the stress-state near the crack. The partial differential equation of the cracked beam nonlinear vibrations is analyzed by Galerkin technique. As a result, the system of piecewise- linear ordinary differential equations is derived with small parameters. The multiple scales method is used to obtain nonlinear vibrations close to the second principal resonance. As a result of this asymptotic transformation, the system of nonlinear modulation autonomous equations is derived. The frequency response is described by fixed points of these modulation equations. These fixed points are obtained by combination the shooting technique and continuation method. This combination of methods is used to analyze the cranked beam under the action of concentration force with constant part. Due to the presence of this constant part of the concentration force, the frequency response has region of multivaluedness.