DETECTING A PREY IN A SPIDER ORB WEB

Author(s)

Kawano, Alexandre ^[1] ; Morassi, Antonino ^[2]

Affiliation

^[1] Univ Sao Paulo, Escola Politecn, Sao Paulo - Brazil

^[2] Univ Udine, Polytech Dept Engn & Architecture, Udine - Italy

• Document type: Journal article
• Source: SIAM JOURNAL ON APPLIED MATHEMATICS; v. 79, n. 6, p. 2506-2529, 2019.
• Web of Science Citations: 1

Abstract

We consider the inverse problem of localizing a prey hitting a spider Orb Web from dynamic measurements taken near the center of the web, where the spider is supposed to stay. The actual discrete Orb Web, formed by a finite number of radial and circumferential threads, is modeled as a continuous membrane. The membrane has a specific fibrous structure, which is inherited from the original discrete web, and it is subject to tensile prestress in the referential configuration. The transverse load describing the prey's impact is assumed of the form g(t)f(x), where g(t) is a known function of time and f(x) is the unknown term depending on the position variable x. For axially symmetric Orb Webs supported at the boundary and undergoing infinitesimal transverse deformations, we prove a uniqueness result for f(x) in terms of measurements of the transverse dynamic displacement taken on an arbitrarily small and thin ring centered at the origin of the web, for a sufficiently large interval of time. The theoretical result is illustrated by means of a numerical implementation of the identification method. (AU)

• FAPESP's process: 17/06452-1 - Uniqueness in the identification of sources in spider webs, Euler-Bernoulli continuous beams and in Germain-Lagrange plates
• Grantee: Alexandre Kawano
• Support Opportunities: Regular Research Grants
• FAPESP's process: 17/07189-2 - Dynamic behavior of spider orb-webs and related inverse problems
• Grantee: Alexandre Kawano
• Support Opportunities: Research Grants - Visiting Researcher Grant - International