Abstract: In this paper, a physical model of elastic beam system with end nonlinear elements coupling is established. From the energy perspective, the vibration-governing equations of the elastic beam system are established based on the generalized Hamilton principle and variational procedure. Firstly, the Galerkin method is employed to expand the transverse vibration displacements of the elastic beam system and establish its residual equation, and the Runge-Kutta algorithm is used to solve the numerical results. Then, on the basis of ensuring the correctness of the calculated numerical results, the influence of the end-coupled nonlinear element on the frequency response of the elastic beam system is investigated in depth, and the influence of the end-coupled nonlinear element on the vibration response of the elastic beam system under the single-frequency excitation is explored, and the generating mechanism of the nonlinear dynamics of the elastic beam system is revealed. Finally, the vibration energy transfer characteristics of the elastic beam system under complex nonlinear vibration response are investigated. The results show that the reasonable utilization of end nonlinear element can exhibit the phenomenon of vibration energy transfer from the active beam to the passive beam, reducing the active beam vibration, and the passive beam is similar to an absorber. Under the complex nonlinear vibration state, the elastic beam system appears the phenomenon of targeted energy transfer, and the quasi-periodic vibration state is the sign of the phenomenon. The emergence of the targeted vibration energy transfer phenomenon provides a possibility to unidirectionally control the vibration level of the elastic beam system from the time domain perspective.