Study on Nonlinear Vibration of Carbon Nanotube-Reinforced Composite Beam Using Nonlocal Beam Theory in a Complex Environment - Bogdan Marinca; Nicolae Herisanu; Vasile Marinca (Applied Sciences)
The present research analyzed the nonlinear vibration of a CNTRC embedded in a nonlinear Winkler–Pasternak foundation in the presence of an electromagnetic actuator and mechanical impact. A higher-order shear deformation beam theory was applied to various models, as well as Euler–Bernoulli, Timoshenko, Reddy, and other beams, using a unified NSGT. The governing equations were obtained based on the extended shear and normal strain component of the von Karman theory and a Hamilton principle. The system was discretized by means of the Galerkin–Bubnov procedure, and the OAFM was applied to solve a complex nonlinear problem. The buckling and bending problems were studied analytically by using the HPM, the Galerkin method in combination with the weighted residual method, and finally, by the optimization of results for a simply supported composite beam. These results were validated by comparing our results for the linear problem with those available in literature, and a good agreement was proved. The influence of some parameters was examined. The results obtained for the extended models of the Euler–Bernoulli and Timoshenko beams were almost the same for the linear cases, but the results of the nonlinear cases were substantially different in comparison with the results obtained for the linear cases.