This paper focuses on the nonlinear dynamic responses of a functionally graded material (FGM) truncated conical shell under 1:2 internal resonance relation. The FGM truncated conical shell is subjected to the in-plane load and the aerodynamic load along the meridian direction. According to a power-law distribution, the material properties are assumed to be modified along the thickness direction smoothly and continuously and the material properties are temperature dependent. The aerodynamic load is obtained by the first-order piston theory with the curvature correction term. According to von Karman type nonlinear geometric relations, first-order shear deformation shell theory, Hamilton principle, the nonlinear equations of motion for the FGM truncated conical shell are established. Furthermore, the nonlinear equations of motion are reduced into a system of the ordinary differential equations by utilizing Galerkin procedure. The multiple scales method is used to obtain the averaged equations for the FGM truncated conical shell under the relations of 1:2 internal resonance and 1/2 subharmonic resonance. The frequency–response curves, time history diagrams, phase portraits, Poincare maps and bifurcation diagrams with different parameters are yielded by employing numerical calculations. The influences of exponent of volume fraction, Mach number, damping coefficient and in-plane load on the nonlinear resonance behaviors of the FGM truncated conical shell are investigated. The chaotic and periodic motions of the FGM truncated conical shell have been discussed in detail.

本文重点研究功能梯度材料（FGM）截顶圆锥壳在1：2内部共振关系下的非线性动力响应。FGM截顶圆锥壳沿子午线方向承受平面载荷和气动载荷。根据幂律分布，假定材料特性沿厚度方向平滑且连续地改变，并且材料特性与温度有关。通过一阶活塞理论和曲率校正项获得气动载荷。根据von Karman型非线性几何关系，一阶剪切变形壳理论，Hamilton原理，建立了FGM截头圆锥壳的非线性运动方程。此外，利用Galerkin过程将非线性运动方程简化为常微分方程组。在1：2内部共振和1/2次谐波共振的关系下，采用多尺度方法获得了FGM截顶圆锥壳的平均方程。通过数值计算可以得到具有不同参数的频率响应曲线，时程图，相位图，庞加莱图和分叉图。研究了体积分数，马赫数，阻尼系数和面内载荷对FGM截头圆锥壳非线性共振行为的影响。FGM截锥形壳体的混沌运动和周期性运动已被详细讨论。