Complex component mode synthesis method using hybrid coordinates for generally damped systems with local nonlinearities. (23rd June 2020) - Wang, Tao; He, Jincheng; Hou, Shuo; Deng, Xi; Xi, Chen; He, Huan
Abstract: In numerous engineering structures with local nonlinearities, the nonlinear effects are usually localized and most parts of the structures behave linearly. Considering this, a reduced-order modelling technique for generally damped systems with localized nonlinearities is proposed. Firstly, the linear parts with non-proportional damping of the system is separated to form one component, which can be formulated in state space and transformed into the modal coordinates using its linear vibration complex modes. The residual flexibility matrix, which can be formulated by using a set of equivalent higher-order complex modes, has been developed to improve the accuracy by capturing the effects of the neglected higher-order complex modes. Secondly, the rest regions of the system form another component behaving nonlinearly, which is kept in its original form to adopt the entire set of nonlinear terms. Next, the second-order differential synthesis equation can be obtained by using compatibility conditions at the junctions. In order to calculate dynamic response of the system, the aforementioned synthesis equation needs to transform into the first-order differential equation because of the singularity of the equivalent mass matrix. Finally, two numerical examples are given to illustrate the effectiveness and the efficiency of the presented method.