Abstract
Research on nonlinear dynamics analysis is a crucial topic in mechanical and aerospace engineering. The analysis of nonlinear normal modes (NNMs) provides us with an effective mathematical tool for interpreting complex nonlinear vibration phenomena. Unlike the invariant normal modes of linear systems, NNMs often exhibit frequency-energy dependence and cannot be computed using the traditional eigen-decomposition method. Calculating NNMs relies on numerical methods that involve expensive iterative computations especially for systems of a large number of degrees of freedom. To relieve computational costs, this paper proposes a mode selection method for the component mode synthesis technique to enable compact reduced-order modeling of structures with localized nonlinearities. The reduced-order model is then combined with a numerical continuation scheme to establish a low-cost NNM analysis framework. This framework can efficiently predict the NNMs of high-dimensional finite element models. In this work, the proposed framework is demonstrated on an I-shaped cantilever beam with localized nonlinear stiffness. The results show that the proposed approach can identify the key modes in the reduced-order modeling procedure. The NNMs of the nonlinear I-shaped beam structure can then be analyzed with significant reduction in computational costs.