Nonlinear vibration behavior of CNTRC plate with different distribution of CNTs under hygrothermal effects

Abstract Hygrothermal effects and periodic loading often occur in carbon nanotube-reinforced composite (CNTRC) during their service life. For the effective use of such materials for high-performance applications, their nonlinear vibration behavior under hygrothermal effects should be clearly understood. Firstly, this paper establishes a nonlinear vibration mechanical model of the CNTRC plate with different distributions of carbon nanotubes (CNTs). Then, ordinary differential equations of nonlinear vibration are given by using the Galerkin method and solved by using the harmonic balance method; additionally, a primary resonance and stability of the CNTRC plate under transverse harmonic loads are analyzed by employing the multi-scale method. Finally, for a fixed shear deformation function, effects of geometric size, volume fraction, CNT distribution, and damping coefficient on the nonlinear vibration behaviors of the CNTRC plate are discussed.