Nonlinear vibration analysis and stability analysis of rotor systems supported on SFD by combining DQFEM, CMS and IHB methods

• Published in: Applied mathematical modelling 2023-09, Vol.121, p.828-842
• Main Authors: Han, Yongnam, Ri, Kwangchol, Yun, Cholil, Kim, Kumchol, Kim, Kwangchol
• Format: Article
• Language: English
• Subjects: Differential quadrature finite element method · component mode synthesis · incremental harmonic balance method · squeeze-film damper · nonlinear vibration ·multi-degree of freedom systems
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2023.05.033

•We proposed a methodology to perform vibration analysis of rotor systems that exhibit localized nonlinearities.•The motion equation of the whole system uses hybrid coordinates.•The stability analysis of the obtained solutions is performed by the floquet theory. In this paper, the differential quadrature finite element method (DQFEM), component mode synthesis (CMS) method and incremental harmonic balance (IHB) method are combined to propose a methodology to perform vibration analysis and stability analysis of rotor systems supported on fluid-film bearings that exhibit localized nonlinearities such as squeeze-film damper (SFD). In multi-degree of freedom systems with SFD, a method for dynamic analysis of the system by reducing the degrees of freedom is first suggested in this paper. DQFEM are used to create the mass matrix, stiffness matrix, and gyroscopic matrix of the system. Then, the system is divided into linear system and nonlinear system, and the motion equation of the linear system reduces the degrees of freedom using the free interface CMS method, and the motion equation of the nonlinear system is written without reducing the degrees of freedom. By synthesizing the equations of motion of each component, the motion equation of the entire system is created. That is, the motion equation of the whole system uses hybrid coordinates. The motion equation of the system is solved using the modified IHB method. To evaluate the effectiveness of the suggested method, the computed solutions are compared with the results presented in the previous literature, and the results are very consistent. Also, stability analysis of the obtained solutions is performed by the Floquet theory. The method suggested in the paper can be effectively used to analyze the dynamic behavior of rotor systems exhibiting localized nonlinearities such as SFD.