Summary
This paper presents a novel method for the computation of nonlinear normal modes (NNMs) of nonlinearly damped dynamical systems based on the combination of force appropriation technique and efficient path following method (EPFM) which is a variant of pseudo arc length continuation method. Pseudo arc length continuation method is one of the most powerful methods for the computation of NNMs but its application is limited to conservative system. The authors extended the application of the EPFM for the computation of linearly damped nonlinear normal by the aids of force appropriation technique (FAT) previously. The method is called FAT-EPFM. In this manuscript the FAT-EPFM is further extended to compute nonlinearly damped normal modes. It was observed that the previously FAT-EPFM fails to compute the nonlinearly damped normal modes, so a mode indicator function (MIF) was utilized in the method to compute nonlinearly damped normal modes. In order to investigate the capability of the method, the nonlinear normal modes of vanderpole system was computed. The results show that FAT-EPFM could calculate the nonlinear normal modes and limit cycle of vanderploe system very well.
