Determination of the prey impact region in a spider orb-web from in-plane vibration

In this paper we study the inverse problem of locating a prey in a spider orb-web from measurements of the in-plane dynamic response of the web immediately after the impact. The orb-web, having axial symmetry and fixed boundary, is described by a continuous pre-stressed membrane undergoing infinitesimal deformation. The impact of the prey is modeled by an in-plane pressure field, whose two spatial components constitute the unknowns of the inverse problem. A reconstruction algorithm for the impact region is proposed, which is essentially based on the determination of certain generalized Fourier coefficients of the loading terms starting from discrete in-plane dynamical measurements that mimic what the spider performs in nature. The results show that the information gathered by the spider positioned at the center of the web is sufficient for a precise localization of the prey, for different prey and orb-web characteristics. The simulations also show that the sensitivity of the reconstruction to errors on the data is significant only when the observation time is close to the theoretical minimum time