In this paper, the investigation of transverse vibration characteristics of the simply supported beam with nonlinear resonators is carried out to address the problem of transverse vibration control of the simply supported beam structure. Firstly, a nonlinear resonator-beam coupling vibration model is established, and the nonlinear vibration differential equations of the system are derived based on Hamilton's principle. The complete semi-analytical solution of the amplitude-frequency response of the system is obtained by using the incremental harmonic balance method and the arc length extension method, and the stability of the solution is analysed by combining with the Floquet theory. The investigation results show that the nonlinear resonator reduces the dimensionless peak of the first-order modes of the simply supported beam from 3.30 to 0.26 under the appropriate parameter values, with a reduction of 92.12%, and does not generate new resonance peaks; the nonlinear stiffness and linear stiffness of the nonlinear resonator determine the vibration reduction frequency location, and the existence of linear stiffness is easy to induce new resonance peaks in the target frequency band.