2D optimum distribution of carbon nanotubes to maximize fundamental natural frequency of polymer composite micro-beams

A new two-dimensional (2D) optimum distribution of carbon nanotubes (CNTs) in the longitudinal and thickness directions of a polymer composite micro-beam is obtained to achieve its highest fundamental natural frequency given a weight percent (wt.%) of CNTs. To this end, optimum distribution patterns are first studied individually in the longitudinal and the thickness directions by dividing the micro-beam into multiple segments and multiple layers, respectively. It is assumed that each segment/layer is made of low-viscosity, thermosetting polyester epoxy/amine resin LY-5052 and reinforced by multi-walled carbon nanotubes. A user-defined code, written in the Python language, is compiled with ABAQUS to generate a three-dimensional finite element model of the micro-beam and subsequently to evaluate the optimum CNT distributions under various boundary conditions. It is found that fundamental frequencies of the clamped–free, clamped–guided and clamped–clamped micro-beams can be enhanced up to 19.5%, 16.8% and 14.8%, respectively, by choosing the 2D optimum CNT distribution profile along the longitudinal and the thickness directions of the micro-beam. The results also reveal that the 1D through-axis and 2D optimal CNT distribution patterns depend on the type of boundary condition applied. However, the optimum through-thickness distribution pattern is found to be independent of the type of boundary condition, which can be of high value for practical applications.