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Non-linear vibration response of functionally graded circular cylindrical shells subjected to thermo-mechanical loading

机译：功能梯度圆柱壳在热机械载荷作用下的非线性振动响应

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摘要

The analysis of the non-linear vibration response is carried out for functionally graded (FG) circular cylindrical shells subjected to thermal environment along with mechanical in-plane non-uniformly distributed loading along the edges and harmonic radial force. The temperature dependent material properties of the simply supported shell are assumed to vary in the radial direction according to power-law distribution. Based on the first-order shear deformation theory and von-Karman type geometric nonlinearity, the strain-displacement relationships are established for circular cylindrical shells. The coupled governing equations of motion for functionally graded cylindrical shells are then derived using Hamilton's principle. Employing Galerkin's method, the coupled partial differential equations of motions are reduced to a set of non-linear ordinary differential equations. In order to obtain the free and forced vibration response of the FG shell, the incremental harmonic balance method, in conjunction with the arc-length method, is used. The non-uniform in-plane loading is converted to Fourier series and the pre-buckling analysis is performed to determine the stress distribution within the shell. The non-linear frequency-amplitude response is studied to examine the effects of volume fractions of the constituents, static partial edge loadings, thermal loads, and radial periodic loadings.
机译：对功能梯度（FG）圆柱壳在热环境下以及沿边缘的机械面内非均匀分布载荷和谐波径向力进行了非线性振动响应分析。假定简单支撑的外壳的温度相关材料属性会根据幂律分布在径向方向上发生变化。基于一阶剪切变形理论和von-Karman型几何非线性，建立了圆柱壳的应变-位移关系。然后，使用汉密尔顿原理导出功能梯度圆柱壳的耦合运动控制方程。采用加勒金（Galerkin）方法，将运动的耦合偏微分方程简化为一组非线性常微分方程。为了获得FG壳体的自由振动和强制振动响应，将增量谐波平衡方法与弧长方法结合使用。平面内的非均匀载荷被转换为傅立叶级数，并进行了预屈曲分析以确定壳内的应力分布。研究了非线性频率-振幅响应，以检查成分的体积分数，静态部分边缘载荷，热载荷和径向周期性载荷的影响。

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