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.

在碳纳米管增强复合材料（CNTRC）的使用寿命期间，经常会发生湿热效应和周期性载荷。为了有效地将此类材料用于高性能应用，应清楚了解其在湿热效应下的非线性振动行为。首先，建立了碳纳米管分布不同的碳纳米管板的非线性振动力学模型。然后，利用Galerkin方法给出了非线性振动的常微分方程，并通过谐波平衡法对其进行了求解。另外，采用多尺度方法分析了横向谐波载荷下CNTRC板的一次共振和稳定性。最后，对于固定的剪切变形函数，几何尺寸，体积分数，CNT分布的影响，