Detecting a prey in a spider orb-web from in-plane vibration Articles uri icon

publication date

  • November 2021

start page

  • 2297

end page

  • 2322

issue

  • 6

volume

  • 81

International Standard Serial Number (ISSN)

  • 0036-1399

Electronic International Standard Serial Number (EISSN)

  • 1095-712X

abstract

  • 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. 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 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 knowledge of the in-plane dynamic response inside an annulus centered at the origin of the orb-web, where the spider is assumed to stay for a sufficiently large registration time, allows us 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.

subjects

  • Materials science and engineering

keywords

  • inverse problems; identification of sources; spider orb-web model; membrane; infinitesimal vibration