The invention discloses a turboshaft engine pneumatic connection multi-rotor coupling vibration analysis method, and belongs to the field of aero-engine vibration analysis. The objective of the invention is to solve problems that there is no mechanical connection between a turbomachine gas generator rotor and a free turbine rotor, the speed ratio between the rotors cannot be accurately obtained, and the free-turbine rotor is not a typical rotor-bearing-anchor support form. According to the method, a unary linear regression analysis method is used for carrying out segmentation processing on anengine typical test run rotating speed curve to obtain an unary segmentation function as a rotating speed ratio calculation basis; The motor-bearing/reduction gear-receiver model is used for carryingout vibration response analysis on the engine rotor system, extracting the vibration amplitude of the outer surface of the rotor impeller and analyzing the typical working condition vibration mode. The method comprehensively considers the operation condition of the engine and the structural characteristics of the turboshaft engine, and can effectively and accurately analyze the vibration responsecondition of the turboshaft engine in the operation transfer subsystem.