Forghani Mohammad Amin, Abdellahi Ramin, Esmaeili Mohsen, Alizadehsani Roohallah, Pławiak Paweł
Department of Mechanical Engineering, Shiraz Branch Islamic Azad University, Shiraz, Iran.
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran.
PLoS One. 2025 Jun 4;20(6):e0323442. doi: 10.1371/journal.pone.0323442. eCollection 2025.
A modified couple stress theory (MCST)-based microshell model for functionally graded graphene platelets reinforced composite (FG-GPLRC) is proposed for the first time to investigate the nonlinear forced vibration behavior of reinforced microshells subjected to extreme temperatures. To achieve this, the effective elastic modulus is derived using the modified Halpin-Tsai model, while the rule of mixtures is applied for density, Poisson's ratio, and thermal expansion coefficients. The first-order shear deformation theory (FSDT) and von Karman strains are considered, and nonlinear governing partial differential equations (PDEs) are derived using Hamilton's principle, which accounts for size effects and initial stresses induced by the thermal environment. The Galerkin method, coupled with the multiple timescale method (MSM), is employed to solve the PDEs and obtain the nonlinear frequency-amplitude curve for primary resonance. The accuracy of the method is validated by comparison with previous research. The study examines the influence of GPL weight fraction, thickness distribution, temperature variations, geometric ratios, and material length scale parameters on the amplitude-frequency curves of nanocomposite cylindrical microshells. The results show that increasing the GPL content and the material length scale parameter leads to higher resonance frequencies. Additionally, while the small-scale parameter amplifies nonlinearity, an increase in the GPL content, especially near the inner and outer surfaces of the shell, reduces the nonlinearity of the reinforced composite. These findings provide valuable benchmarks for evaluating the performance of alternative methods.
首次提出了一种基于修正偶应力理论（MCST）的功能梯度石墨烯片增强复合材料（FG - GPLRC）微壳模型，以研究在极端温度下增强微壳的非线性强迫振动行为。为此，使用修正的Halpin - Tsai模型推导有效弹性模量，而混合法则用于密度、泊松比和热膨胀系数。考虑了一阶剪切变形理论（FSDT）和冯·卡门应变，并使用汉密尔顿原理推导非线性控制偏微分方程（PDEs），该原理考虑了热环境引起的尺寸效应和初始应力。采用伽辽金方法并结合多时间尺度方法（MSM）来求解偏微分方程，并获得主共振的非线性频率 - 振幅曲线。通过与先前研究的比较验证了该方法的准确性。该研究考察了GPL重量分数、厚度分布、温度变化、几何比和材料长度尺度参数对纳米复合圆柱微壳振幅 - 频率曲线的影响。结果表明，增加GPL含量和材料长度尺度参数会导致更高的共振频率。此外，虽然小尺度参数会放大非线性，但GPL含量的增加，特别是在壳的内表面和外表面附近，会降低增强复合材料的非线性。这些发现为评估替代方法的性能提供了有价值的基准。
