Vibration analysis of functionally graded carbon nanotubes reinforced composite nanoplates

Dang Van Hieu; Nguyen Thi Kim Thoa

doi:10.59400/n-c.v2i1.381

Open Journal Systems

Vibration analysis of functionally graded carbon nanotubes reinforced composite nanoplates

Dang Van Hieu, Nguyen Thi Kim Thoa

Abstract

This work presents the analytical analysis for free linear vibration behavior of functionally graded-carbon nanotubes reinforced composite (FG-CNTRC) nanoplates in the framework of nonlocal strain gradient theory (NSGT) and the first-order shear deformation plate theory (FSDPT). The nanoplate is considered made of a mixture of an isotropic polymer matrix and reinforced carbon nanotubes (CNTs). Four different distributions of CNTs are examined including uniformly distributed and FG reinforcements (FG-O, FG-X, and FG-V). The governing equations of motion are established based on the Hamilton’s principle. The closed-form analytical solution for the natural frequency of FG-CNTRC nanoplates with simply supported all edges is carried out by using the Navier-type solution. The impact of some key parameters on the natural frequencies of FG-CNTRC nanoplates is also studied and discussed. The result shows that FG-CNTRC nanoplates reveal the softening- or hardening-stiffness effects depending on the relationship between the nonlocal parameter and the material length scale parameter. The aspect ratios of FG-CNTRC nanoplates, the volume fraction, and the distribution pattern of CNTs have also an important impact on the vibration behavior of FG-CNTRC nanoplates.

Keywords

nonlocal strain gradient; nanoplate; free vibration; nanotubes; reinforcement; first-order shear deformation

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DOI: https://doi.org/10.59400/n-c.v2i1.381
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