Abstract: The turbine test rig system for a heavy-duty gas turbine consists of a test rig and a test piece. The dynamic characteristics of the test piece are represented as mechanical impedance at the interface between the test rig and the test piece. The impedance matching principle of mechanical impedance synthesis analysis at this location is utilized to determine the mutual influence of the damped critical speeds, thus the design limitation conditions of the unknown test piece are obtained. Meanwhile, the dynamic models of the test pieces and the test rig are established to obtain the damped critical speed of the system. The results validate the effectiveness of the design constraints for controlling transverse vibration damped critical speeds in the test piece. These conclusions provide guidance for the design of turbine test pieces.