An analysis is performed in this research to examine the thermally induced vibrations in skew cylindrical shells. It is assumed that shell is made from a composite laminated material where each layer is reinforced with graphene platelets (GPLs). The amount of GPLs in the layers may be different which results in a piecewise functionally graded media. The one-dimensional transient heat conduction equation is established through the thickness of the shell. Heat conduction equation is solved using the finite difference method for each layer and continuity of temperature and heat flux is applied between the layers. Crank Nicolson algorithm is implemented to obtain the temperature profile at each time step and after that thermally induced force and moment are evaluated. The kinematics of the shell are estimated following the first order shear deformation shell theory. Also it should be noted that an oblique coordinates system in addition to orthogonal system is defined which make it easier to apply the boundary conditions. The definition of strain and kinetic energies are constructed and Following the Ritz method whose shape functions are estimated by Chebyshev polynomials, energies are provided in discrete form of the governing equations. Results of this study are provided to explore the effects of thermal and mechanical boundary conditions, geometry of the shell, weight fraction and distribution patterns of GPLs. It is highlighted that thermally induced vibrations indeed exist especially in thin class of shells.

中文翻译：

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由 FG-GPLRC 制成的斜圆柱壳在快速表面加热下的振动


本研究进行了分析，以检查斜圆柱壳中的热致振动。假设外壳由复合层压材料制成，其中每层都用石墨烯片（GPL）增强。各层中 GPL 的数量可能不同，这会导致分段功能分级媒体。建立了贯穿壳体厚度的一维瞬态热传导方程。使用有限差分法对每层求解热传导方程，并在层之间应用温度和热通量的连续性。实施曲柄尼科尔森算法以获得每个时间步长的温度分布，然后评估热感应力和力矩。壳的运动学根据一阶剪切变形壳理论进行估计。还应该注意的是，除了正交系统之外，还定义了斜坐标系，这使得更容易应用边界条件。构建了应变和动能的定义，并遵循形状函数由切比雪夫多项式估计的 Ritz 方法，以控制方程的离散形式提供能量。本研究的结果旨在探索热和机械边界条件、壳体几何形状、GPL 的重量分数和分布模式的影响。值得注意的是，热致振动确实存在，尤其是在薄壳中。