Nonlocal couple stress-based quasi-3D nonlinear dynamics of agglomerated CNT-reinforced micro/nano-plates before and after bifurcation phenomenon

In present research exploration, the nonlinear dynamic stability characteristics of axially compressed nanocomposite plates at micro/nano-scale reinforced with randomly oriented carbon nanotubes (CNTs) are investigated within the both prebuckling and postbuckling regimes. To accomplish this examination, the nonlocal couple stress (NCS) continuum elasticity is incorporated to a quasi-3D plate theory which separates the plate deformation to the bending and shear parts considering simultaneously the transverse shear and normal displacements. In addition, a two-parameter homogenization scheme is utilized to obtain the effective characters of the randomly oriented CNT-reinforced nanocomposites. The NCS-based nonlinear differential equations of motion are discretized using the Kronecker tensor product together with the shifted Chebyshev-Gauss-Lobatto gridding pattern. Thereafter, the Galerkin technique together with the pseudo arc-length continuation method are employed to achieve the NCS-based fRequency-load and nonlinear frequency ratio-deflection curves before and after of the bifurcation point. It is deduced that for a randomly oriented CNT-reinforced heterogeneous micro/nano-plate in which the most CNTs are located inside clusters, increasing the value of cluster volume fraction leads to increase a bit the significance of the softening and stiffing characters related to the nonlocal and couple stress tensors before the bifurcation phenomenon, but it causes to decrease them after the critical bifurcation point. Opposite patterns before and after the bifurcation phenomenon are predicted for the agglomeration in which the most CNTs are located outside clusters.

Automated summary

In this study, the nonlinear dynamic stability characteristics of axially compressed nanocomposite plates reinforced with randomly oriented carbon nanotubes (CNTs) at micro/nano-scale were investigated. The nonlocal couple stress (NCS) continuum elasticity was incorporated to a quasi-3D plate theory to consider the transverse shear and normal displacements. A two-parameter homogenization scheme was used to obtain the effective characters of the CNT-reinforced nanocomposites. The NCS-based nonlinear differential equations of motion were discretized using the Kronecker tensor product and the shifted Chebyshev-Gauss-Lobatto gridding pattern. The results showed that the significance of the softening and stiffening characters related to the nonlocal and couple stress tensors increased slightly before the bifurcation phenomenon, but decreased after the critical bifurcation point.