Detecting a prey in a spider orb-web from in-plane vibration

Spiders perform a task similar to solving an inverse problem when detecting the position of a prey, a mate or a predator perturbing the orb-web. Some recent work has advanced in the study of the orb-web as a sensor when it is subjected to small transverse vibrations, using a continuous membrane model for the orb-web. However, in-plane vibrations have not been investigated yet as data for the prey's detection problem. In the present work, we develop the structure of the small in-plane vibratory response of an axially symmetric orb-web supported at the boundary. Additionally, we prove that the knowledge of the in-plane dynamic response inside an annulus centered at the origin of the orb-web, where the spider is supposed to stay, for a sufficiently large registration time, allows to determine uniquely the in-plane distributed load simulating the prey's impact. The theoretical outcome is illustrated with a numerical implementation of the reconstruction method.