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.