Nonlinear primary resonance behaviors of rotating FG-CNTRC beams with geometric imperfections

This study aims at investigating the geometric imperfection sensitivity of nonlinear primary resonance behaviors of a rotating functionally graded carbon nanotube reinforced composite (FG-CNTRC) beam. Three kinds of imperfections containing sine, global, and local types are represented by a general function. In view of the von-Kármán geometric nonlinearity assumption, the nonlinear forced vibration equation of rotating imperfect FG-CNTRC beams is established. For the purpose of capturing more accurate results, the high-order Galerkin discretization is adopted. Subsequently, the nonlinear primary resonance behavior of this rotating system is explored by the method of multiple scales. Then, combined influence of FG-CNTRCs, rotating motion, and geometric imperfections on the nonlinear resonance responses are examined. It is observed that the hardening-type nonlinearity of this system can be transformed into the softening-type nonlinearity on account of the initial imperfection. However, the other parameters cannot change the nonlinearity type. Furthermore, the imperfection and rotating motion have coupled effects on the nonlinear resonance responses, and inversely have independent effects on the natural frequencies. Meanwhile, when the geometric imperfection exists, the hardening behavior of the resonance curve is turned to the softening one by raising the Galerkin discretization order. This phenomenon indicates that single-order discretization leads to erroneous qualitative and quantitative assessments of nonlinear resonance responses.