A hybrid power series and artificial bee colony algorithm (PS-ABC) method is applied to solve a system of nonlinear differential\r\nequations arising from the distributed parameter model of multiwalled carbon nanotube (MWCNT) cantilevers in the vicinity of\r\nthin and thick graphite sheets subject to intermolecular forces. The intermolecular forces are modeled using van derWaals forces. A\r\ntrial solution of the differential equation is defined as sum of two polynomial parts. The first part satisfies the boundary conditions\r\nand does contain two adjustable parameters. The second part is constructed as not to affect the boundary conditions, which\r\ninvolves adjustable parameters. The ABC method is applied to find adjustable parameters of trial solution (in first and second\r\npart). The obtained results are compared with numerical results as well as analytical solutions those reported in the literature.\r\nThe results of the presented method represent a remarkable accuracy in comparison with numerical results. The minimum initial\r\ngap and the detachment length of the actuator that does not stick to the substrate due to the intermolecular forces, as important\r\nparameters in pull-in instability of MWCNT actuator, are evaluated by obtained power series.
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