This article deals with the computational modeling of nonlinear rotor dynamic systems. The theoretical basis of the modal method, and combination with the method of dynamic compliances supplemented by the method of trigonometric collocation, is presented. The main analysis is focused on the solutions of transient and steady state responses. The algorithms for solving this range of problems are presented. The finite element method is the basis for both methods. The theoretical analysis is supplemented with a solution of an example model.

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