Double modal synthesis method applied in analyzing large-size nonlinear systems

Numerical methods for calculating steady state forced responses of nonlinear systems is considered in this study. In this work we have proposed a double modal synthesis method. Reduction are performed in two steps. The first was applying branch mode synthesis on the assembled structures. The second was a nonlinear modal reduction by retaining only the primary nonlinear modes of the reduced model. In this way, the nonlinear calculation can be considerably accelerated. Effective modal parameters were then derived and saved in forms of interpolation functions of modal amplitudes. Complex modal amplitudes were obtained by resolving the decoupled nonlinear functions depending on effective modal parameters. Two substructures connected by a cubic nonlinear interface were employed to validate the proposed methodology. Results showed that the accuracy of method was sensible to the choice of the reduction basis. This approach can be applied to similar systems with local nonlinearities.