Maximum natural frequencies of polymer composite micro-beams by optimum distribution of carbon nanotubes

Optimum distribution of multi-walled carbon nanotubes (MWCNTs) within a polymer composite micro-beam is sought to achieve its highest natural frequencies given a weight percent (wt.%) of MWCNTs. To this end, the micro-beam is divided into ten segments which are perfectly bonded to their neighbors. Each segment is made of low-viscosity, thermosetting polyester epoxy/amine resin LY-5052 and is reinforced by MWCNTs. A computer program, written in the Python programming language, is compiled with ABAQUS to generate a three-dimensional (3D) finite element (FE) model of the micro-beam and subsequently to evaluate an optimum CNT distribution under various vibration modes and boundary conditions. The influence of uniform and optimum MWCNT distributions on the natural frequencies, mode shapes and equivalent stiffness of the micro-beams is investigated and the results are compared with those of the pure polymer micro-beam. Subsequently, after acquiring the optimum distribution of the MWCNTs, two new CNT dispersion functions are proposed for maximizing fundamental frequencies of the clamped-free and clamped–clamped micro-beams. The results of the FE analysis reveal that the optimal reinforcement distribution pattern significantly depends on vibration mode shapes, particularly the micro-beam curvature under each mode. It is observed that fundamental frequencies of clamped-free, clamped-guided and clamped–clamped micro-beams are enhanced up to 15.9%, 13.1% and 12.6%, respectively, by choosing optimum MWCNT distribution profiles along the micro-beam length.