Keywords: multi-degree of freedom systems, nonlinear components, fault diagnosis, coherence analysis.

In engineering practice, many mechanical and structural systems can be represented by a multi-degree of freedom (MDOF) model. A MDOF system can behave nonlinearly simply due to the nonlinear characteristic of one component within the system. In many practical cases, such a nonlinear component may represent a fault. Typical examples of these include beams, rotor shafts, and multi-storey buildings [1,2]. Therefore, locating nonlinear components in MDOF systems has considerable significance in the fault diagnosis of a wide range of engineering systems and structures.

Coherence is a frequency domain concept, which has been widely used to examine the extent to which the relationship between two response signals is linear or nonlinear at a particular frequency. Recently the authors proposed a new concept known as the nonlinear output frequency response functions (NOFRFs) [3] and revealed a series of important properties of MDOF nonlinear systems via studying the NOFRFs of MDOF systems [4,5]. These properties can relate the linear and nonlinear relationship between the responses of two masses to the location of nonlinear component in MDOF nonlinear systems. By exploiting these properties, a coherence analysis based approach is developed in this paper for locating nonlinear component in MDOF systems.

The proposed approach evaluates the values of a coherence related index for all consecutive masses and determines the location of nonlinear component in MDOF nonlinear systems from the results. Numerical simulation studies verify the effectiveness of the approach. Because a nonlinear component in practical MDOF systems may represent a fault or abnormal condition, the approach can be used to address the fault diagnosis issues of MDOF engineering systems and structures when random excitations can be applied to test systems for fault diagnosis.

1

A. Neild, P.D. Mcfadden, M.S Williams, "A discrete model of vibrating beam using time-stepping approach", Journal of Sound and Vibration, 239, 99-121, 2001. doi:10.1006/jsvi.2000.3158

2

T.G. Chondros, A.D. Dimarogonas, J. Yao, "Vibration of a beam with breathing crack", Journal of Sound and Vibration, 239, 57-67, 2001. doi:10.1006/jsvi.2000.3156

3

Z.Q. Lang, S.A. Billings, "Energy transfer properties of nonlinear systems in the frequency domain", International Journal of Control, 78, 354-362, 2005. doi:10.1080/00207170500095759

4

Z.K. Peng, Z.Q. Lang, S.A. Billings, "Analysis of Multi-Degree-of-Freedom nonlinear systems using nonlinear output frequency response functions", Journal of Sound and Vibration, under review, 2007.

5

Z.K. Peng, Z.Q. Lang, "Detecting the position of nonlinear component in periodic structures from the system responses to dual sinusoidal excitations", International Journal of Non-Linear Mechanics, 42, 1074-1083, 2007. doi:10.1016/j.ijnonlinmec.2007.06.002

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