Nonlinear Normal Modes of structures with nonlinear material based on Independent Periodic Method

Abstract

Ever-increasing demands of the modern world and the growth of industry requirements toward more accurate analyses have made the engineering community develop the first fundamental step and meet the needs by extending the previous prevalent linear methods into nonlinear areas. In this regard, the improvement of linear modes as one of the most pervasive and widespread analytical methods opens a new window to analyses with more closeness to reality. In this paper, after the deep identification of Nonlinear Normal Modes, an approach is proposed to analyze the multi-degree-of-freedom structures with nonlinear material under undamped free vibration. Afterward, through an in-depth investigation of the calculation methods, a novel algorithm for identifying Nonlinear Normal Modes was proposed, and by expanding this algorithm to the existing invariable motion equation used in free vibration analysis, the possibility of the extraction of all Nonlinear Normal Modes has emerged. After that, to investigate the functionality of the proposed approach, the Finite Elements Method-based Model of a 2-story steel structure was developed and, after verification, it was used to form the invariable differential equations. Finally, after verifying the Independent Periodic Method, pseudo-continuous masses of Nonlinear Normal Modes and Frequency-Energy curves of the mentioned structure were calculated. It is worth noting that the independency of resulted response to previous points, the possibility of capturing Nonlinear Normal Modes with different frequencies in each degree-of-freedom, the potential of capturing all internal resonances, the expendability of Finite Elements Model to a set of invariable motion equations, and considering material nonlinearity are among achievements of the current paper.