Original scientific paper
An approximate response of the large system with local cubic nonlinearities subjected to harmonic excitation
Jianshe Luo
Xiaoying Liu
Abstract
This paper considers a multi-degree-of-freedom mechanical system with local cubic nonlinearities. A major concern is placed on nonlinear dynamic behaviors of the system subjected to a soft harmonic excitation under primary resonance condition. The classical model reduction method associated with the single modal resonance theory is employed to investigate the system and obtain a reduced dynamic model with only a single DOF (degree of freedom) under resonance condition. In the case of the soft excitation, the analytical expression of dynamic response and the frequency response characteristic equation can be derived from the reduced model of the system using the harmonic balance method. Some qualitative and quantitative results are then obtained. An example of ten-story nonlinear shear structure is included. Results from the reduction method of the system are in good agreements with those obtained from the numerical integration of the dynamic equation of the original system. This paper demonstrates an effective way in fast analysis of the multi-DOFs nonlinear system qualitatively and quantitatively, especially large scale multi-DOFs system at primary resonance state.
Keywords
multi-DOFs; nonlinear dynamic behavior; local cubic nonlinearities; model reduction; harmonic resonance
Hrčak ID:
133249
URI
Publication date:
21.1.2015.
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