The suppression of the dynamic response of a beam structure is studied under a single harmonic displacement excitation.By attaching a damping spring support to the structure and using the modal complex effect caused by non-classical damping， the system vibration is effectively localized. The structural displacement response is described by using the Wave Propagation Ap?proach， and the traveling wave’s propagation is constrained only in the left region of the viscoelastic support. Then， the spatial separation of the traveling and standing waves appears within the beam， and the directional propagation of the vibration energy is eventually achieved. The waveform conversion， energy storage and flow in the structure are analyzed by the vibration power flow method， and the flow direction of the vibration energy is determined， which may help reveal the mechanism of the vibration energy transformation. The dissipation effect of the damping spring support on the vibration energy of the beam structure is analyzed in detail， and the transmission law of the vibration energy upon the wave separation is discussed. Through a typical example， the effect to suppress structural vibration response is fully demonstrated by using a damping spring support， and the vibration suppression and energy dissipation of the different design schemes are compared.