Nonlocal strain gradient-based quasi-3D nonlinear dynamical stability behavior of agglomerated nanocomposite microbeams

Abstract

An efficient numerical quasi-3D beam model is introduced to analyze the effect of carbon nanotube (CNT) agglomeration on the nonlinear dynamical stability characteristics of agglomerated beams at microscale made of agglomerated CNT-reinforced nanocomposites. For this objective, the constructive material properties are estimated based upon a micromechanical homogenization scheme containing only two parameters to capture the associated agglomeration of randomly oriented CNTs, while the nonlocal strain gradient continuum theory of elasticity is enrolled to apprehend various size dependency features. The unconventional nonlinear governing differential equations of motion are solved numerically via the shifted Chebyshev-Gauss-Lobatto discretization pattern together with the pseudo-arc-length continuation strategy. The size-dependent frequency-load-deflection characteristic curves are traced corresponding to different degrees of agglomeration including complete and partial ones. It is revealed that for an agglomerated CNT-reinforced nanocomposite microbeam in which the most CNTs are inside clusters, a higher value of the cluster volume fraction results in to reduce the significance of the softening and stiffing characters associated with the nonlocal and strain gradient small-scale effects, respectively. However, for an agglomerated CNT-reinforced nanocomposite microbeam in which the most CNTs are outside clusters, increasing the value of the cluster volume fraction plays an opposite role in the size dependency features.