# Large-Amplitude Vibrations of Spider Web Structures
## 3 Results and Discussions
### Linear Free Vibration of Spider Web
#### 3.1.1 Effect of Structural Patterns  
There are three cases considered: the effect of a variation in radial thread number; the effect of a form of capture area; and the effect of a variation in capture thread number. Since the variation in thread number changes the mass and stiffness of the web, the natural frequencies and their fundamental mode shapes of the spider web are also changed. Firstly, the variations of radial threads were investigated. Figure 6 presents the patterns considered in this study. The differences between these three cases are the number of radial threads. It is noted that there are 8, 12 and 16 radial threads for patterns 1, 2, 3, respectively. Figure 7 presents the natural frequencies for the spider web with a different number of radial threads. By increasing the number of radial threads, natural frequencies of different mode shape are generally increased. Mode shapes 8 and 9 have a cross over phenomenon when the patterns change from pattern 2 to pattern 3. In addition, the corresponding mode shapes of patterns 1, 2, and 3 are presented in Figure 8. It should be noted that changing the pattern by increasing the number of radial treads does not have a significant effect in lower mode as the mode shapes are almost similar for all patterns. However, it is interesting to note that the snap through behaviour, which is the jump of shape from one to another configuration, can be observed in modes 6 and 9. Figure 6: Patterns 1, 2 and 3 of spider web model. Figure 7: Natural frequencies of spider web patterns 1, 2, and 3. Secondly, the effects of shapes of capture threads have been considered. The patterns 1 and 4 are compared as shown in Figure 9. For pattern 1, the form of capture area is a straight spiral thread while those for pattern 4 is concentric circles. The variation of natural frequencies, influenced by the form of capture threads, is depicted in Figure 10. At the first three modes, the natural frequencies remain almost the same, but after mode 4, it becomes obvious that spider web with a straight spiral capture thread has higher natural frequencies than those with a concentric circle capture thread. It can also be explained that, as the spider web structure sustains only axial deformation, the structure with curved member could trigger the follower force and its orientation, leading to buckling behaviour so easily. This illustrates that the straight spiral thread is likely to provide more stiffness and stability to the structure rather than a circular shape of capture thread. The first three corresponding mode shapes are presented in Figure 11.  
Figure 8: Mode shapes of patterns 1, 2 and 3: (**a**) mode 1(**b**) mode 2 (**c**) mode 3. Figure 9: Patterns 1 and 4 of spider web model. Moreover, the effects of the number of capture thread were studied. Figure 12 presents the patterns 4, 5, and 6 of spider web. It should be noted that there are 10, 20 and 30 capture threads for patterns 4, 5 and 6, respectively, which means that the spacing between the capture threads is 0.03, 0.015, and 0.01 m for pattern 4, 5 and 6, respectively. As the number of capture threads increases, the mesh width decreases. Figure 13 portrays the variation of natural frequencies of spider webs with the different number of capture threads. In contrast to the results of the increase in radial threads, the natural frequencies of all mode shapes are decreased while the number of capture threads increased. This sort of result shows that the increment of capture threads only significantly changes the mass of the spider  
Figure 11: Mode shapes of patterns 1 and 4: (**a**) mode 1 (**b**) mode 2 (**c**) mode 3. Figure 10: Natural frequencies of spider web patterns 1 and 4.  
web structure, while the stiffness of the structure is not obviously affected. The corresponding mode shapes of patterns 4, 5, and 6 are compared in Figure 6:0 It is clear that adding more capture threads results in changing the vibration amplitude and structural stability.