# Large-Amplitude Vibrations of Spider Web Structures
## 1 Introduction  
The function of a spider web is to capture and hold a rapidly flying insect, which shows that the spider web has excellent flexibility and resilience. Two aspects of the design of the web make this possible: the optimised spider silk and the design of the web. Spider silk is one ofthe bio-inspired materials that have shown excellent performance exceeding artificial materials in their properties [1]. There has been interest in adopting the spider web's engineering properties in defence technology and medical applications, including microscopes, telescopes and bomb guiding systems [2]. Considering it on a weight to weight basis, its tensile strength is sometimes even stronger than steel and some silks are almost as elastic as rubber. On this ground, silks provide two to three times toughness of synthetic fibres such as nylon or Kevlar. Unlike man-made polymers, spider silk can improve in strength without compromising fracture toughness [3]. Besides the superior material properties of spider silk, spider web structures themselves can be recognised as a pre-stressed system called tensegrity (tensional integrity) structures [4]. This sort of structure shows a unique combination of geometry and mechanic properties, and as a result of the optimal distribution of structural mass, they are highly efficient structures. It is the nature of spider web structures to quickly absorb the energy as well as constrain drastic oscillations due to the prey impact [5]. The experiments on energy absorption and dissipation of spider web subjected to flying prey have been studied considering different species of spiders [6; 7; 8]. Moreover, localised damage is a universal feature of spider webs. When a spider web is subjected to local loading, failure is limited to the loading threads and the loaded thread becomes a sacrificial element to keep the majority of the web remains intact, and spider webs strength after slightly damaged [9]. The spider web is so resilient because of its distinctive combination of strength and stretchiness and the geometrical arrangement of the web. It is noted that the properties of spider silk have been fully studied [10; 11; 12]. However, many researchers only focused on the outstanding properties of silk rather than the spider web's structure itself.  
It is noticeable that the spider web could experience large deformation due to wind load or prey trapping [13]. It should be noted that the spider web should be able to trap large prey. This effect allows the web to absorb high kinetic impacts that would otherwise cause an extension above the elastic range and therefore destroy the web. The single degree of freedom experiment has been performed to evaluate the stiffness and damping decay of spider web and it is found that the overall stiffness of the spider web tends to be nonlinear under shock load [14]. Nevertheless, the studies of the structural behaviour using advanced finite element modelling regarding the vibration characteristics of spider webs have not been fully investigated. Hence, this study investigates the large amplitude free vibration behaviour of the spider web structure. This better insight into its engineering performance can unleash its applications in battle and defence technology. The large-deformable finite element 3D models of spider web structures with and without geometric nonlinearities are developed using Abaqus. According to the virtual work-energy theory, the model is formed from the strain energy owe to axial deformation, kinetic energy owes to the spider web movement and the virtual work due to the self-weight per unit unstretched length, and the concept of large-strain, the large-deformation principle has been used to evaluate natural frequencies and corresponding mode shapes with geometric nonlinearity. To analyse the performance of spider webs, several parametric studies of the effect of different patterns, elastic modulus, density, and inertia moment were carried out.