Analysis of the vibration characteristics of a variable cross section rotor using the complex transfer matrix method and comparison with different methods

Today, gas turbine engines are preferred in many areas, including civil and military, in the aviation industry. Due to the high-speed operation of the gas turbine, some vibration problems arise in the rotor structure. The most important of these are the unbalanced load caused by the centrifugal force, the modal shapes of the shaft due to the flexible beam structure, and the critical velocity values. To solve these problems during and after the design process, the modal analysis of the rotor is very important. In this study, a mathematical model of a rotor-bearing system with two discs of variable cross-section was created using the complex transfer matrix method (CTMM) to measure the responses in the bearings in both axes and compared with classical methods. Newton Raphson method was used to obtain the solution of the model created with CTMM. The critical velocity values found were compared with the finite element method and it was seen that the values found matched with the analytical method with a maximum error of 2.97%. As a result of this analysis, it has been determined that the TMM method offers 4.75 times faster solutions for this model than the finite element method. As a result, in this study, it has been shown that CTMM will be more advantageous in rotor design than other methods thanks to its faster solution advantage.