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Abstract：
A time-dependent third-order shear deformation theory (TSDT) approach on the displacements of thick functionally graded material (FGM) conical shells under dynamic thermal vibration is studied. Dynamic equations of motion with TSDT for thick FGM conical shells are applied directly with the partial derivative of variable R*θ in the curve coordinates (x, θ, z) instead of y in the Cartesian coordinates (x, y, z) for thick FGM plates, where R* is the middle-surface radius at any point on conical shells. The generalized differential quadrature (GDQ) numerical method is used to solve the dynamic differential equations in equilibrium matrix forms under thermal loads. It is the novelty of the current study to identify the parametric effects of shear correction coefficient, environment temperature, TSDT model, and FGM power law index on the displacements and stresses in the thick conical shells only subjected to sinusoidal heating loads. The physical parts with values on the length-to-thickness ratio equals 5, and 10 FGMs can be used in an area of an airplane engine that usually operates near more than 1000 K of temperatures when the thermal stress is considered and affected. The important findings of the presented study are listed as follows. The values of normal stress are in decreasing tendencies with time in cases when the coefficient c1 equals 0.925925/mm2 in TSDT and length-to-thickness ratio equals 5. The shear stress values in x plane z direction on the minor middle-surface radius (r) equals the major middle-surface radius (R) over 8 and length-to-thickness ratio equals to 5 can withstand T = 1000 K of pressure.
摘要：
研究了动态热振动下厚功能梯度材料（FGM）锥形壳位移的时变三阶剪切变形理论（TSDT）方法。厚FGM锥形壳的TSDT运动动力学方程直接应用于曲线坐标中变量R*θ的偏导数（x，θ,z)而不是直角坐标中的y(x,y,z)对于厚FGM板，其中R*是圆锥壳上任意点的中间曲面半径。采用广义微分正交(GDQ)数值方法求解热载荷下平衡矩阵形式的动态微分方程。识别剪切校正系数的参数效应是当前研究的新颖性，环境温度,TSDT型号,和FGM幂律指数关于仅承受正弦热载荷的厚锥形壳中的位移和应力。长度与厚度比的值等于5的物理零件，并且当考虑和影响热应力时，可以在通常接近1000K以上温度的飞机发动机区域中使用10FGM。本研究的重要发现如下。在TSDT中系数c1等于0.925925/mm2且长度与厚度之比等于5的情况下，法向应力值随时间呈下降趋势。在x平面z方向上，次要中间表面半径（r）上的剪切应力值等于8上的主要中间表面半径（R），长度与厚度之比等于5，可以承受T=1000K的压力。
