Quasi-3D nonlinear primary resonance of randomly oriented CNT-reinforced micro/nano-beams incorporating nonlocal and couple stress tensors

Abstract

In the current research examination, the nonlinear primary resonance of softly periodic excited nanocomposite micro/nano-beams containing nanofillers agglomeration is analyzed incorporating geometrical nonlinearity. To fulfill this motivation, the nonlocal couple stress (NCS) theory of continuum elasticity is formulated within the framework of the quasi-3D beam model integrating different size dependency features together with the geometrical nonlinearity. The associated constructive material properties are captured based upon a micromechanical homogenization scheme containing only two parameters to take the associated agglomeration of randomly oriented carbon nanotubes (CNTs) into account. The solution of the obtained unconventional nonlinear governing differential equations of motion is then achieved numerically by putting the shifted Chebyshev-Gauss-Lobatto discretization pattern in conjunction with the pseudo-arc-length continuation strategy. The NCS-based frequency-response and amplitude-response characteristic curves associated with the primary resonance are tracked down relevant to various degrees of agglomeration including complete and partial ones. It is indicated that by increasing the CNT amount inside clusters, the height of predicted jump feature increases and its peak tends to a higher ratio of excitation frequency to natural frequency. Additionally, it is demonstrated that by decreasing the cluster volume fraction, the soft excitation amplitudes at the bifurcation points enhance, especially at the first one.