Purpose

Free vibrations of non-homogenous (functionally graded material (FGM)) axisymmetric nonlocal thermoelastic hollow sphere has been taken into consideration for investigation. The material of nonlocal thermoelastic sphere is supposed to be graded using power law in radial direction.

Methods

The solution of continued power series is employed to resolve the differential equations and to investigate the analytical solutions for field functions i.e. temperature, stress and displacement.

Results and Conclusions

The analytical results have been authenticated using numerical computations with computer based software like MATLAB. The numerical results have been shown graphically for the comparison of frequency shift and thermoelastic damping for local and nonlocal elastic materials. Deduction of results has been validated with the already published literature.

中文翻译：

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FGM型非局部弹性球体在广义热弹性中的自由振动分析

目的

为了研究，已经考虑了非均匀（功能梯度材料（FGM））轴对称非局部热弹性空心球的自由振动。非局部热弹性球体的材料应该使用幂律在径向上进行分级。

方法

连续幂级数的解用于求解微分方程，并研究温度，应力和位移等场函数的解析解。

结果与结论

使用基于计算机的软件（例如MATLAB）进行数值计算，可以验证分析结果的准确性。数值结果已以图形方式显示，用于比较局部和非局部弹性材料的频移和热弹性阻尼。结果的推论已经用已经发表的文献进行了验证。