Abstract A study on radial vibrations of functionally graded, isotropic, thermoelastic, thick-walled hollow sphere due to a thermal load has been carried out in the context of non-Fourier law of heat conduction (LS model). The material and thermal parameters have been assumed to vary according as simple power-law function of the radial coordinate. Closed-form solution to the problem has been derived with the aid of Laplace transform and elimination procedure. The inverse Laplace transforms of radial displacement and temperature have been obtained by employing the theory of residues. The solution in case of uncoupled and classical coupled thermoelasticity has been obtained directly by deducing the results of present analysis. The deduced results have been validated with the benchmark results available in the literature. Also the radial stress, hoop stress, temperature gradient for various grading parameters at different radial distances have been computed and presented graphically for validating and giving more emphasis on these field quantities. A significant effect of grading parameter on the stress and temperature gradient produced in the sphere has been noticed. A comparative analysis has been done for homogeneous and functionally graded spheres.

中文翻译：

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热负荷引起的功能梯度球的径向振动

摘要 在非傅立叶热传导定律（LS 模型）的背景下，对热载荷引起的功能梯度、各向同性、热弹性、厚壁空心球的径向振动进行了研究。假设材料和热参数根据径向坐标的简单幂律函数而变化。借助拉普拉斯变换和消元程序，推导出了该问题的闭式解。利用残差理论得到了径向位移和温度的拉普拉斯逆变换。通过推导目前的分析结果，直接得到了非耦合和经典耦合热弹性情况下的解。推导出的结果已经用文献中可用的基准结果进行了验证。还有径向应力，环向应力、不同径向距离的各种分级参数的温度梯度已被计算并以图形方式呈现，以验证和更加强调这些场量。已经注意到分级参数对球体中产生的应力和温度梯度的显着影响。对均质和功能分级的球体进行了比较分析。