Nonlinear forced vibration and detached resonance curves of axially moving functionally graded carbon nanotube reinforced composite plates.

In this paper, the nonlinear forced vibration responses of axially moving functionally graded carbon nanotube reinforced composite (FG-CNTRC) rectangular thin plates are investigated. In the frame of classical plate theory and von Kármán geometric nonlinear theory, the nonlinear partial differential equations of motion for axially moving FG-CNTRC plates are established by Hamilton's principle and discretized through the Galerkin method. The validity of the present model is verified by comparing the natural frequencies and the critical divergence velocity of the axially moving plate with the existing results in the literature. The frequency response curves (FRCs) of axially moving FG-CNTRC plates subjected to transverse harmonic concentrate excitation are calculated by using the incremental harmonic balance (IHB) method. The stability and bifurcation characteristics of period solutions obtained through the IHB method are analyzed by Floquet theory. The isolated detached resonance curves (DRCs) are observed inside the main continuous FRCs of axially moving FG-CNTRC plates. Saddle-node bifurcation, Hopf bifurcation, quasi-periodic motion and the internal resonance caused by the modal coupling effect are analyzed. The numerical results illustrate the effects of the CNT distribution, volume fraction, axially moving velocity, aspect ratio and width-to-thickness ratio on the nonlinear dynamic responses of axially moving FG-CNTRC plates. [ABSTRACT FROM AUTHOR]