This paper examines the 1:1:1 internal resonant nonlinear dynamic characteristic of the simply supported varying thickness functionally graded graphene platelets reinforced composite (FG-GPLRC) smart truncated sandwich conical shell subject to the combined effects of transverse load and in-plane force. The truncated smart sandwich conical shell is composed of an FG-GPLRC varying thickness core and two magneto-electro-elastic face layers, whose material properties and constitutive relations are individually identified by the rule of mixture, improved Halpin-Tsai approach and generalized Hooke's law. Utilizing the first-order shear deformation theory (FSDT), von Karman's geometrical nonlinearity, Hamilton's principle and Galerkin technique, the 3DOF dimensionless nonlinear dynamic formulations for the truncated smart FG-GPLRC conical shell are established. The multiple-scale technique is applied to developing the averaged equations for the truncated smart FG-GPLRC conical shell under combined resonance. The frequency-response and force-response curves, Poincare maps, phase portraits, time history diagrams, bifurcation and maximum Lyapunov exponent diagrams can be portrayed by the nonlinear equation solver and Runge-Kutta approach. The effects of the damping and tuning parameters, transverse and in-plane forces on the 1:1:1 internal resonant nonlinear dynamic characteristic of truncated smart varying thickness FG-GPLRC sandwich conical shell are examined.

中文翻译：

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智能 FG-GPLRC 夹层变厚度截断圆锥壳的非线性动力学特性，前三阶模式具有内部共振


本文研究了简支可变厚度功能梯度石墨烯片状增强复合材料 （FG-GPLRC） 智能截短夹层锥形壳在横向载荷和面内力综合作用下的 1：1：1 内部共振非线性动力学特性。截断智能夹芯圆锥壳由一个FG-GPLRC变厚芯和两个磁-电-弹性面层组成，其材料性质和本构关系分别由混合法则、改进的Halpin-Tsai方法和广义胡克定律标识。利用一阶剪切变形理论 （FSDT）、von Karman 几何非线性、汉密尔顿原理和 Galerkin 技术，建立了截断智能 FG-GPLRC 圆锥壳的 3DOF 无量纲非线性动力学公式。该多尺度技术被应用于开发组合谐振下截断智能 FG-GPLRC 圆锥壳的平均方程。频率响应和力-响应曲线、庞加莱映射、相位图、时间历史图、分岔和最大李雅普诺夫指数图可以通过非线性方程求解器和 Runge-Kutta 方法来描述。研究了阻尼和调谐参数、横向力和面内力对截断智能变厚度 FG-GPLRC 夹芯锥形壳体 1：1：1 内部谐振非线性动力学特性的影响。