Abstract
This article deals with computational modeling of nonlinear rotor dynamic systems. The theoretical basis of the method of dynamic compliances and the modal method, supplemented by the method of trigonometric collocation, are presented. The main analysis is focused on the solutions of the eigenvalue problem and steady‐state and transient responses. The algorithms for solving this range of problems are presented. The finite element method, the method of dynamic compliances, and the modal method are supplemented by the trigonometric collocation method. The theoretical analysis is supplemented by the solution of a model task, which is focused on the application of the trigonometric collocation method. The solution of a technical application, which is a pump, is presented in this article.
Highlights
This article deals with computational modeling of nonlinear rotor dynamic systems
The finite element method, the method of dynamic compliances, and the modal method are supplemented by the trigonometric collocation method
It is possible to include experimental data in the solution, especially the dynamic compliance of the stator, which is possible to include in the analysis of rotor dynamic systems
Summary
Brno University of Technology, Faculty of Mechanical Engineering, Brno, Czech Republic. The modal method presented in this article is based on a reduction in frequency domain, so choosing a higher number of modes does not lead to a higher order of matrixes. Nataraj and Nelson (1989) presented a general approach to this method It describes the use of modal reduction to decrease the matrix order. SOLUTION OF TRANSIENT RESPONSE The equation to describe the motion of linear rotor systems (especially the free shaft part for future analysis) has the form. The solution of this equation in time step t, including initial conditions, may be written in matrix form (Yang, 1996). In the time step, j + 1, it takes the form of j
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