Nonlinear dynamics of rotating box FGM beams using nonlinear normal modes

In this work an analysis is performed on the nonlinear planar vibrations of a functionally graded beam subjected to a combined thermal and harmonic transverse load in the presence of internal resonance. Adopting the direct perturbation MMS technique, the partial differential equations of motion of the beam are reduced to sets of first-order nonlinear modulation equations in terms of the complex modes of the beam. The assumption of steady-state values of centrifugal loads is evaluated. It has to be said that there is a lack of information about modeling of rotating box beams made of functionally graded materials (FGMs) under thermo-mechanical loads. The influence of the transverse load amplitude and the internal detuning parameter on the strength of nonlinear modal interaction is illustrated. It is also shown that the system exhibits periodic and quasiperiodic responses for a typical range of parameter values.

► We study the internal resonance phenomenon of functionally graded material of a beam structural model.
► We use nonlinear modes in the perturbation technique.
► Numerical simulations show a complex dynamic scenario and detect chaos.
► Chaotic attractors undergo attracting-merging and boundary crises.