Abstract
This paper deals with a method to study closely the stationary solution of non-linear dynamic systems at several degrees of freedom (dof) subjected to harmonic excitations with or without parametric modifications. This solution is obtained basically with the utilisation of an iterative algorithm adapted to the first approximation of Newton–Raphson method. This method is based on the exploitation of the eigensolutions of the associated conservative linear system with or without parametric modifications as well as on the characteristics of localised non-linearities and finally on the exploitation of the equivalent linearisation method. With the application of this method at first on linear models initially condensed by modal synthesis, the predictions of non-linear responses can be obtained rapidly. In a second step, this method is adapted to a condensed linear model used in the first optimisation procedure of the non-linear dynamic behaviour. In fact, before the non-linear analysis, the appropriate choice of the basis of reduction, that is referred to as “robust” obtained from the initial linear system is necessary. This robust basis will be used as condensation basis of the modified model local per zone or global by substructure leads to a prediction of vibratory responses of complex structures greatly modified and affected by localised non-linearities.
At the end of this article, two examples are given to illustrate the efficiency and the performances of the proposed method.