Abstract

In the present study a wavelet-based procedure is applied for the parametric identification of a nonlinear discrete cable model on the basis of experimental data obtained from free-vibration dynamic tests. The 3D cable dynamics is described by two partial integro-differential equations in the transversal planar and nonplanar displacement components. By expanding such variables in series of linear eigenfunctions, a discrete model is obtained by applying a classical Galerkin procedure. The resulting set of nonlinear ODEs contains quadratic and cubic coupling terms. The core of the identification technique is the discretization of such nonlinear differential equations by means of orthogonal Daubechies scaling functions. The Wavelet-Galerkin solution of the nonlinear equation involving the scaling function expansion of nonlinear terms leads to an algebraic problem that has to be inverted in order to solve for the vector of unknown parameters. A sdof model able to describe the in-plane unimodal oscillations is considered. Numerical and experimental identification tests are presented. Accurate estimates of the linear and quadratic parameters are achieved from the moderate oscillation amplitude response of an experimental discrete cable-mass model. The accuracy of the cubic parameter estimate is shown to depend on the level of both the oscillation amplitude and noise.

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