Investigation of the Effects of Dimensional Inaccuracies on the First Natural Frequency of Cellular Lattice Structures

Lattice structures have attracted a great deal of attention for being used in different industries due to unique properties such as high strength-to-weight ratio and high damping coefficient. These metamaterials might suffer from dimensional inaccuracies, i.e., variable strut’s diameter, wavy struts, micropores, and deviation from the designed cross-sectional area, which arise from the fabrication process. These inaccuracies can drastically affect their mechanical response. In this paper, the effects of different dimensional inaccuracies, including variable struts’ diameter, wavy struts, and material concentration at nodes, on the frequency response of different cellular lattice structures are studied. To do so, a finite element model is constructed using Timoshenko beam elements, and the natural frequencies are obtained for four different lattices. The obtained results show that, by increasing the average diameter, the natural frequency increases drastically, whereas by increasing the amount of variation in the struts’ diameter and waviness the natural frequency decreases by a small amount. It is also observed that the lattice structures whose main deformation mechanism is axial loading are more sensitive to the change of average struts’ diameter. In addition, the natural frequency increases as the concentration of material in the vicinity of the nodes increases. The effect of material concentration inaccuracy is more pronounced for the first lattice for which the number of struts meeting at one node is the smallest.