Effects of geometric nonlinearities on the coupled dynamics of CNT strengthened composite beams with porosity, mass and geometric imperfections

This study investigates the effects of geometric nonlinearities on the dynamical behaviour of carbon nanotube (CNT) strengthened imperfect composite beams by considering both axial and transverse motions. For the given general model of the beam, the system modelling has been adopted from the literature and the nonlinear dynamic response in presence of an external harmonic load is examined for the first time in the case of axially functionally graded (AFG) CNT fibre, which is used for strengthening the structure. Porosity imperfection with the ability to vary though the thickness is modelled using simple, closed and open-cell models; the porosity variation is formulated using uniform, linear, symmetric and un-symmetric models. The geometrical imperfection is considered by allowing the beam to have an initial curved longitudinal axis and the mass imperfection is modelled by introducing a concentrated mass at a certain point of the beam. Using a combination of the Galerkin scheme together with dynamic equilibrium technique, the influence of different imperfections and porosities on the frequency response of the system is examined. It is shown that, for the case of AFG CNT strengthened beam, geometrical imperfection can change the nonlinear response from a hardening to a softening behaviour. Besides, the importance of considering the interaction between axial and transverse motion is examined in detail. The influence of lumped mass imperfection and its position is also studied showing that this type of imperfection can change the nonlinear behaviour of the system significantly. Moreover, the influence of increasing the CNT volume fraction and functionally spreading the CNTs through the length is discussed. The results are useful for analysing the resonance phenomena in strengthened structures facing various imperfections. Graphic abstract: [Figure not available: see fulltext.]