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Damage detection in nonlinear systems using an improved describing function approach with limited instrumentation

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Abstract

The describing function approach is a powerful tool for characterizing nonlinear dynamical systems in the frequency domain. In this paper, we extend the describing function approach to detect and localize the damage in initially healthy nonlinear systems with limited measurements. The requirement of complete FRF of the underlying linear system by describing function approach is overcome by using a newly developed nonparametric principal component analysis-based model. Numerical simulation studies have been carried out by considering a cantilever beam with multiple local nonlinear attachments to demonstrate the localization process of the improved describing function approach with limited instrumentation. Parametric estimation of a shear building model is considered as a second numerical example to demonstrate the capability of the proposed approach in identifying the different types of nonlinearities and as well as combined types of nonlinearities (i.e. more than one type of nonlinearity). These combined nonlinearities can exist either in the same or different spatial locations. Experimental investigations have also been presented in this paper to complement the numerical investigations to demonstrate the practical applicability.

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Acknowledgements

This paper is being published with the permission of the Director, CSIR-Structural Engineering Research Centre (SERC), Chennai. The authors would like to acknowledge the support received from Shri S. Harish Kumaran of ASTAR Lab, Shri D. Deivaraj and Shri M. Karunamoorthi of SHML laboratory, CSIR-SERC, while carrying out the experiments presented in this paper.

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  1. CSIR-Structural Engineering Research Centre, CSIR Campus, Chennai, TN, India

    J. Prawin & A. Rama Mohan Rao

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  1. J. Prawin
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Correspondence to A. Rama Mohan Rao.

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Appendix

Appendix

See Table 6.

Table 6 Describing function for different types of nonlinearity
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Prawin, J., Rao, A.R.M. Damage detection in nonlinear systems using an improved describing function approach with limited instrumentation. Nonlinear Dyn 96, 1447–1470 (2019). https://doi.org/10.1007/s11071-019-04864-3

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