Abstract: The turbine test rig system of heavy-duty gas turbine consists of a test rig and a test piece. It is necessary to meet the experimental requirements of different test pieces for the test rig. Therefore, when a new test piece is designed, its influence on the unbalanced response of the test rig must be considered. The dynamic characteristics of the test piece considered as the mechanical impedance at the location of the test rig and the test piece, and the impedance matching principle of mechanical impedance composite method at the location is utilized to determine the mutual influence of the damped unbalanced response, thus the design limitation conditions of the unknown test piece are obtained. Meanwhile, the dynamic model of a test piece and the test rig is established, to obtain the damped unbalanced response of the system, and the results verify the effectiveness of the design limitation conditions of the damped unbalanced response of transverse vibration of the test piece.