Asymmetrical Spider Orb Webs

The study of the mechanisms guiding the spider in prey capture and gathering information through web vibration is one of the main objectives of current research in this field. Recent studies have provided partial insights, primarily through the development of a mechanical model of the spider web represented as a continuous fiber membrane with an appropriate pre-tensile stress state and undergoing small deformations. To date, all analytical results available in the literature – both in modelling and in the inverse problem of prey identification – have been restricted to axially symmetrical webs. In this work, we move beyond the axial symmetry assumption and address the more realistic case of vertical asymmetry, a characteristic of almost all vertical orb webs. This generalization introduces non-trivial challenges in mechanical and mathematical modelling. We establish the well-posedness of the statical response for a class of asymmetrical orb webs in a suitable weighted Sobolev space and we investigate the dynamically forced problem via eigenfunction expansion.