In order to improve the flow induced vibration of the adjustable central flap mechanism deployed in the second throat in the working state, a SMA (shape memory alloy) self-resetting vibration damping device which could meet the limited installation space of the central flap mechanism was designed and manufactured according to the biasing two-way driving principle of SMA. The SMA constitutive relation subroutine compiled by UMAT interface was used to realize the numerical analysis of the maximum pressing force of the damping device, and the error between the numerical analysis and the static test results is about 2.58%. A ground vibration reduction test platform was built to test the vibration reduction effect of SMA self-resetting vibration damping device in the separated and closed states. The vibration reduction test results show that the vibration response of the central flap mechanism is significantly reduced with SMA self-resetting damping device activated. An obvious damping effect appear in the frequency band of 0～100 Hz, especially, the damping rate in the range of low frequency to 55 Hz is greater than 50%.