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<p>Bolt loosening is a prevalent issue in engineering structures; however, previous studies have overlooked the influence of the surrounding environment on detuning structures and remain mainly restricted to uni-directional functionally graded materials and classic boundary conditions. To fill these gaps, this study aims to investigate the boundary detuning vibration characteristics of a bi-directional functionally graded graphene oxide powder nano-reinforced composite (FG-GOPRC) cylindrical shell surrounded by a Winkler-Pasternak elastic foundation under arbitrary boundaries. A unified semi-analytic model (SAM) is proposed. To simulate actual bolt loosening, discontinuous arc constraints are developed by refining the traditional artificial spring technique. The radial and axial distribution of graphene oxide powder (GOP) in the matrix is considered, with composite properties determined using the mixture rule and Halpin–Tsai meso-mechanical model. The Winkler-Pasternak elastic foundation simulates structural interaction with the environment, while the first-order shear deformation theory (FSDT) reveals the shell’s constitutive relation. Natural frequencies are derived by combining the Rayleigh–Ritz method with the state space method to solve matrix eigenvalues. For model validation, the strategy of progressive validation is adopted. Model correctness is verified via comparisons with existing literature and finite element method (FEM) results. Moreover, the influences of key parameters such as GOP distribution patterns, elastic foundation, and detuning models on the vibration frequencies of the shell are analyzed. Numerical results indicate that the three types of detuning exhibit significantly different effects on the vibration characteristics of the shell. Among them, coupling detuning has the most pronounced influence, followed by stiffness detuning, while arc-length detuning shows the weakest effect. Moreover, increasing the degree and number of detuning leads to a reduction in natural frequencies. The interaction between detuning and the elastic foundation is also significant, exhibiting either amplifying or mitigating effects depending on the vibration mode.</p>

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Vibration characteristics of bi-directional FG-GOPRC cylindrical shells embedded in elastic foundations with boundary detuning conditions

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Chong Tang,
  • Yufeng Chang,
  • Qingpeng Han,
  • Baosheng Zhao,
  • Yu Wang,
  • Yue Gu,
  • Xiangdong Liu

摘要

Bolt loosening is a prevalent issue in engineering structures; however, previous studies have overlooked the influence of the surrounding environment on detuning structures and remain mainly restricted to uni-directional functionally graded materials and classic boundary conditions. To fill these gaps, this study aims to investigate the boundary detuning vibration characteristics of a bi-directional functionally graded graphene oxide powder nano-reinforced composite (FG-GOPRC) cylindrical shell surrounded by a Winkler-Pasternak elastic foundation under arbitrary boundaries. A unified semi-analytic model (SAM) is proposed. To simulate actual bolt loosening, discontinuous arc constraints are developed by refining the traditional artificial spring technique. The radial and axial distribution of graphene oxide powder (GOP) in the matrix is considered, with composite properties determined using the mixture rule and Halpin–Tsai meso-mechanical model. The Winkler-Pasternak elastic foundation simulates structural interaction with the environment, while the first-order shear deformation theory (FSDT) reveals the shell’s constitutive relation. Natural frequencies are derived by combining the Rayleigh–Ritz method with the state space method to solve matrix eigenvalues. For model validation, the strategy of progressive validation is adopted. Model correctness is verified via comparisons with existing literature and finite element method (FEM) results. Moreover, the influences of key parameters such as GOP distribution patterns, elastic foundation, and detuning models on the vibration frequencies of the shell are analyzed. Numerical results indicate that the three types of detuning exhibit significantly different effects on the vibration characteristics of the shell. Among them, coupling detuning has the most pronounced influence, followed by stiffness detuning, while arc-length detuning shows the weakest effect. Moreover, increasing the degree and number of detuning leads to a reduction in natural frequencies. The interaction between detuning and the elastic foundation is also significant, exhibiting either amplifying or mitigating effects depending on the vibration mode.