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<p>This research explores the nonlinear dynamic behaviors of sigmoid functionally graded (SFG) cylindrical shells (CSs) reinforced with spiral stiffeners (SSs) utilizing a semi-analytical approach. The shell is subjected to a temperature distribution along its thickness, and the material properties of both the shell and stiffeners vary continuously across the thickness in accordance with a power-law distribution and temperature-dependent relations. To model the system, classical shell theory (CST), von Kármán nonlinear kinematics, the smeared stiffener approach, and the Galerkin technique are employed. To examine the system’s vibrational behaviors, the method of multiple scales (MMSs) is applied, targeting internal resonances (1:1/2:1/4) and a superharmonic resonance of order 2/1. This leads to the derivation of a six-degree-of-freedom nonlinear averaged system. This study, for the first time, presents a detailed numerical analysis that uncovers key dynamic behaviors of the system, including waveforms, phase portraits, and Poincaré maps, emphasizing how changes in stiffener angles influence the nonlinear response of the SFG-CSs reinforced with SSs under internal and superharmonic resonances. In addition, the results demonstrate that optimizing the angles of SSs is a viable strategy for enhancing the dynamic stability of the current system.</p>

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Nonlinear dynamics and chaos of sigmoid functionally graded cylindrical shells reinforced with spiral stiffeners under superharmonic and internal resonances

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Kamran Foroutan,
  • Farshid Torabi

摘要

This research explores the nonlinear dynamic behaviors of sigmoid functionally graded (SFG) cylindrical shells (CSs) reinforced with spiral stiffeners (SSs) utilizing a semi-analytical approach. The shell is subjected to a temperature distribution along its thickness, and the material properties of both the shell and stiffeners vary continuously across the thickness in accordance with a power-law distribution and temperature-dependent relations. To model the system, classical shell theory (CST), von Kármán nonlinear kinematics, the smeared stiffener approach, and the Galerkin technique are employed. To examine the system’s vibrational behaviors, the method of multiple scales (MMSs) is applied, targeting internal resonances (1:1/2:1/4) and a superharmonic resonance of order 2/1. This leads to the derivation of a six-degree-of-freedom nonlinear averaged system. This study, for the first time, presents a detailed numerical analysis that uncovers key dynamic behaviors of the system, including waveforms, phase portraits, and Poincaré maps, emphasizing how changes in stiffener angles influence the nonlinear response of the SFG-CSs reinforced with SSs under internal and superharmonic resonances. In addition, the results demonstrate that optimizing the angles of SSs is a viable strategy for enhancing the dynamic stability of the current system.