Dynamic identification of pretensile forces in a spider orb-web

Abstract

In this paper we propose a constructive procedure to determine the radial pretension in an axially-symmetric orb-web, on the basis of one eigenfrequency and its corresponding vibration mode. The method can be applied both to axisymmetric modes, corresponding to the solution of a regular Sturm–Liouville problem, and to non-axisymmetric modes, corresponding to the solution of a singular Sturm–Liouville problem. In the absence of measurement errors of the eigenfunction, the identification of the pretension field is almost perfect. On the contrary, if the measurement presents some noise, then identification is imprecise. In this case, a regularization technique applied to the measurement of the eigenfunction, or to its derivative, is proposed, as well as a filtering process, which significantly improves the reconstruction of the pretension field. The fundamental mode of vibration, sampled with a suitable number of points, is the one that provides the lowest identification error.