This paper is devoted to superharmonic and subharmonic behavior investigation of imperfect functionally graded (FG) cylindrical shells with external FG spiral stiffeners under large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler–Pasternak foundation augmented by a Kelvin–Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. The von Kármán strain-displacement kinematic nonlinearity is employed in the constitutive laws of the shell and stiffeners. The external spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. The coupled governing equations are solved by using Galerkin’s method in conjunction with the stress function concept. The multiple scales method is utilized to detect the subharmonic and superharmonic resonances and the frequency–amplitude relations of the 1/3 and 1/2 subharmonic and 3/1 and 2/1 superharmonic resonances of the system. Finally, the influences of the stiffeners helical angles, foundation type, coefficient of the nonlinear elastic foundation, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

中文翻译：

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基于广义非线性粘弹性基础的螺旋加强非完美 FG 圆柱壳的不对称大变形超谐波和次谐波共振

本文致力于在大振幅激励下研究带有外部 FG 螺旋加强筋的不完美功能梯度 (FG) 圆柱壳的超谐波和亚谐波行为研究。该结构嵌入在广义非线性粘弹性基础中，该基础由双参数 Winkler-Pasternak 基础组成，该基础由具有非线性立方刚度的 Kelvin-Voigt 粘弹性模型增强，以考虑振动硬化/软化现象和阻尼考虑。von Kármán 应变-位移运动非线性用于壳和加劲肋的本构定律。圆柱壳的外螺旋加劲肋采用涂抹加劲肋技术建模。耦合控制方程采用伽辽金法结合应力函数概念求解。利用多尺度方法检测系统的分谐波和超谐波共振以及1/3和1/2分谐波以及3/1和2/1超谐波共振的频率-幅度关系。最后，综合研究了加劲肋螺旋角、基础类型、非线性弹性基础系数、材料分布和激励幅值对系统共振的影响。