Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type

In this paper, an approximate analytic procedure is developed for solving the strong non-linear differential equations of the Duffing type with complex-valued function which describes the dynamical behavior of many real systems. The method is based on the elliptic-Krylov-Bogolubov procedure where the solutions are the Jacobi elliptic functions. As an example, the self-excited vibrations of the rotor with variable shaft rigidity are considered. The analytical results of this example are compared with numerical ones and excellent agreement is found between them. (C) 2001 Elsevier Science B.V. All rights reserved.