Abstract
The volume fraction of the carbon nanotube (CNT) plays a key role in ensuring the performance of the CNT reinforced polymer composite, especially under the severe vibration, which leads to the resonance and failure of the composite structure. In this paper, a bottom-up multiscale method is adopted to study the effect of the CNT volume fractions on the nonlinear vibration of the poly (methyl methacrylate) (PMMA)/CNT composite. According to the molecular simulation, the longitudinal, transverse and shear moduli of the PMMA/CNT nanocomposites are found to increase with the increasing CNT volume fractions. Substituting the simulated moduli into the extended rule of mixtures (EROM), the efficiency parameters of the PMMA/CNT composite with various CNT volume fractions are derived based on a homogenization approach. The derived efficiency parameters are used in the functionally graded (FG)-based EROM to obtain the expressions of the longitudinal, transverse and shear moduli of the macroscopic composite plate, so as to obtain the constitutive equation for the nonlinear vibrations of the FG-based PMMA/CNT composite plate. The subsequent meshless simulation results demonstrate that the natural frequencies of the FG-based composite plate increase with the increasing volume fractions, whereas the ratios of the nonlinear to linear frequencies decrease. Using the bottom-up multiscale analysis, the macroscopic vibration responses are analyzed for the PMMA/CNT composites with the CNT volume fractions up to 9.0%, which provides a paradigm of the design of the PMMA/CNT composite by considering the CNT volume fraction effect.
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