Non-parametric identification of a non-linear buckled beam using discrete-time Volterra Series

The consideration of nonlinearities in mechanical structures is a question of high importance because several common features as joints, large displacements and backlash may give rise to these kinds of phenomena. However, nonlinear tools for the area of structural dynamics are still not consolidated and need further research effort. In this sense, the Volterra series is an interesting mathematical framework to deal with nonlinear dynamics since it is a clear generalization of the linear convolution for weakly nonlinear systems. Unfortunately, the main drawback of this non-parametric model is the need of a large number of terms for accurately identifying the system, but it can be overcomed by expanding the Volterra kernels with orthonormal basis functions. In this paper, this technique is used to identify a Volterra model of a nonlinear buckled beam and the kernels are used for the detection of the nonlinear behavior of the structure. The main advantages and drawbacks of the proposed methodology are highlighted in the final remarks of the paper.