Size-Dependent Nonlinear Free Vibration of Multilayer Functionally Graded Graphene Platelet-Reinforced Composite Tapered Microbeams

PurposeThe article is dedicated to the study of the size-dependent nonlinear vibration characteristics of multilayer functionally graded graphene platelets-reinforced (FG-GPLs) composite tapered microbeams.MethodsThe Timoshenko beam theory (TBT) is applied as the fundamental framework of the theoretical model, integrated with the modified couple stress theory (MCST) and the von Karman geometric nonlinearity hypothesis. The modified Halpin-Tsai micromechanical model and rule of mixture are employed to determine the properties of the composites. Combining Hamilton's principle and isogeometric analysis, the governing equations as well as boundary conditions for the nonlinear characteristics of the tapered microbeam are derived, and the direct iteration technique is employed for the numerical solution.ResultsThe comparative analysis of the calculated values with the results reported in the public literature verifies the accuracy and efficacy of the proposed model and calculation strategy. Then, a detailed parametric investigation is carried out to explore the nonlinear characteristics of FG-GPLs tapered microbeams, and the effects of various factors, including taper ratio, boundary conditions and GPLs distribution patterns, are examined.ConclusionsThe findings showed that the change in the taper ratio along the thickness direction has a greater impact than the change in the taper ratio along the width direction. In addition, the increase of GPLs weight fraction and small-scale parameters will lead to a notable increase in the FG-GPLs tapered microbeam's nonlinear frequency, while the increase in the length-to-thickness ratio has little effect on this value. Meanwhile, regardless of the boundary conditions, the nonlinear frequency ratio corresponds to the X-GPLs distribution pattern is always the largest, followed by the U-GPLs and O-GPLs in order.