Characterization of catastrophic bifurcations in an agglomerated carbon nanotube-reinforced beam

Large amplitude vibrations are inevitable in the life cycle of a composite structure. On the other hand, the large amplitude deflections may give rise to cracks and fractures in the composite structure. Consequently, in order to avoid such issues, in this study, the examination of nonlinear events including bifurcation analysis of a beam structure made of advanced materials exposed to superharmonic excitation is presented, for the first time. In this regard, an unshearable model is developed for an aggregated carbon nanotube-strengthened beam in line with the Eshelby-Mori-Tanaka hypothesis. Making use of the advantage of the direct method of multiple scales, the reduced order equations for the aggregated nanocomposite beam subjected to primary, and superharmonic excitations are disclosed. Some fascinating numerical simulations clarify nonlinear aspects of the aggregated beam under the alterations of agglomeration parameters as well as temperature. It is deduced that the increment of heterogeneity enlarges the maximum quantity of the steady-state response until, two more steady-state responses are generated. Thereafter, the heterogeneity increment reduces the gap between the two stable steady-state responses. After a catastrophic bifurcation, one stable steady-state response remains. The amplitude of the remained steady state response decreases as a consequence of the heterogeneity increment. The aggregation decreases the temperature at which the multi-valued steady-state response zone starts, when the nanocomposite beam is superharmonically excited. Moreover, the heterogeneity doesn't change the maximum steady-state amplitude of the nanocomposite beam undergone superharmonic excitation at a given force frequency. On the other hand, the gap between the two steady state amplitudes of the nanocomposite beam subjected to primary resonance excitation extends as a consequence of the heterogeneity increment.