Large-Amplitude Vibrations of Spider Web Structures

Abstract

Spider silk, as a natural material, shows exceptional performance in its properties. The combination of the superior properties of spider silk and the geometry of spider structures make the spider web very resilient. A spider web structure can be considered as a cable-like structure with inappreciable torsional, bending and shear rigidities. An investigation emphasising on natural frequencies and corresponding mode shapes with and without the consideration of geometric nonlinearity is presented in this paper. This study is the world’s first discovery of large amplitude free vibration behaviours of spider web structures. Large deformable finite element 3D models of spider web structures have been developed and validated. By using the energy method, the variational model of the spider web structures have been established to further extend the finite element model, consisting of the strain energy due to axial deformation, kinetic energy due to the spider web movement and the virtual work caused by the self-weight per unit unstretched length. The emphasis of this study is placed on the linear and geometric nonlinear behaviour of the spider web structures considering different structural patterns and material properties. To determine the large-amplitude free vibrational behaviours, a series of pretension load is applied to the first step in Abaqus to initiate the nonlinear strain-displacement relationships enabling a precursor to free vibrations. The parametric studies stemming from structural patterns (the number of radial and capture threads), elastic modulus, density, and inertia moment have been highlighted. The insight will help engineers and scientists to adapt the concept of spider webs, their geometric properties, and damage patterns for the design of any structural membranes, preventing any failure from dynamic resonances and nonlinear phenomena.