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Research Papers

The Nonlinear Output Frequency Response Functions of One-Dimensional Chain Type Structures

[+] Author and Article Information
Z. K. Peng

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK; State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, P.R.C.pengzhike@tsinghua.org.cn

Z. Q. Lang

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UKz.lang@sheffield.ac.uk

J. Appl. Mech 77(1), 011007 (Sep 30, 2009) (10 pages) doi:10.1115/1.3173604 History: Received August 01, 2007; Revised April 22, 2009; Published September 30, 2009

It is well-known that if one or a few components in a structure are of nonlinear properties, the whole structure will behave nonlinearly, and the nonlinear component is often the component where a fault or an abnormal condition occurs. Therefore it is of great significance to detect the position of nonlinear components in structures. Nonlinear output frequency response functions (NOFRFs) are a new concept proposed by the authors for the analysis of nonlinear systems in the frequency domain. The present study is concerned with investigating the NOFRFs of nonlinear one-dimensional chain type systems, which have been widely used to model many real life structures. A series of important properties of the NOFRFs of locally nonlinear one-dimensional chain type structures are revealed. These properties clearly describe the relationships between the NOFRFs of different masses in a one-dimensional chain type system, and allow effective methods to be developed for detecting the position of a nonlinear component in the system. The results are an extension of the authors’ previous research studies to a more general and practical case, and have considerable significance in fault diagnosis and location in engineering systems and structures.

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Figures

Grahic Jump Location
Figure 1

The NOFRF based representation for the output frequency response of linear systems

Grahic Jump Location
Figure 2

The NOFRF based representation for the output frequency response of nonlinear systems

Grahic Jump Location
Figure 3

A locally nonlinear multidegree freedom oscillator

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