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Nonlinear Behaviour of Structures Using the Volterra Series—Signal Processing and Testing Methods

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Abstract

To extend modal analysis to nonlinear structures, and adopting the Volterra series as a mathematical framework, we present some new routes together with progress on signal processing. The closed form expressions of higher-order transfer function on the other hand would permit one to obtain eigenvalues of various orders and eigenvectors. Existing signal processing analyzers are initially devoted to linear systems. Programs treating input and output signals of systems are tailored for one-time (or frequency) variable functions. Nonlinear systems can indeed be analyzed by one-dimensional (direct or inverse) Fourier transforms. However, the experimenter rapidly discovers their limitation when dealing with coupling phenomena that require functions with many time (or frequency) variables. In this framework, multidimensional Fourier transforms are necessary.

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Authors and Affiliations

  1. I S M C M, Laboratory of Rheology and Structures, 3 Rue F. Hainaut, 93407, Saint-Ouen, France

    I. Tawfiq & T. Vinh

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  1. I. Tawfiq
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  2. T. Vinh
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Tawfiq, I., Vinh, T. Nonlinear Behaviour of Structures Using the Volterra Series—Signal Processing and Testing Methods. Nonlinear Dynamics 37, 129–149 (2004). https://doi.org/10.1023/B:NODY.0000042909.51421.61

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