3/2 superharmonic resonance and 1/2 subharmonic resonance of functionally graded carbon nanotube reinforced composite beams. (1st June 2020)

• Record Type: Journal Article
• Authors: Wu, Zhihua; Zhang, Yimin; Yao, Guo
• Is Part Of: Composite structures. Volume 241(2020)
• Publication Date: 2020-06-01
• Subjects: Functionally graded carbon nanotube reinforced composite -- Timoshenko beam -- Incremental harmonic balance method -- Stability -- 3/2 superharmonic resonance -- 1/2 subharmonic resonance; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2020.112056
• Languages: English
• ISSNs: 0263-8223

Abstract

Abstract: This paper deals with the 3/2 superharmonic resonance and 1/2 subharmonic resonance of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams. In the framework of Timoshenko beam theory and von Kármán type of geometric nonlinearity, the nonlinear equations of motion for FG-CNTRC beams are derived by Hamilton's principle and discretized by the Galerkin method. The incremental harmonic balance (IHB) method is used to calculate the dynamic responses of FG-CNTRC beams subjected to transverse harmonic excitation. The stability of steady state solutions obtained from the IHB method is evaluated by Floquet theory. It is found that when the period-1 solutions of FG-CNTRC beams with asymmetric carbon nanotube distribution lose stabilities and the period doubling bifurcation occurs, the nonlinear system will generate 3/2 superharmonic resonance and 1/2 subharmonic resonance respectively in two specified frequency ratio intervals. The frequency response curves of 3/2 superharmonic resonance and 1/2 subharmonic resonance are constructed by the IHB method. The numerical results reveal the effects of material, geometry and excitation parameters on the 3/2 superharmonic and 1/2 subharmonic resonant responses of the system. Additionally, the two unstable regions where the 3/2 superharmonic and 1/2 subharmonic resonances occur are determined under different parameters.