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基于非Fourier热传导方程,应用镜像方法考虑材料表面对热波的反射作用,采用波函数展开法研究了半无限功能梯度材料中亚表面异质圆柱夹杂的热波散射问题。给出了功能梯度材料中温度分布的一般解。分析了亚表面异质圆柱的几何参数(如夹杂大小、埋藏深度)和热物理参数(如导热系数、非均匀参数等)对功能梯度材料外表面温度的影响。热波可以通过谐和的调制激光加热在材料表面激发。本文可望为功能梯度材料的红外热波无损检测、热物理反问题的研究提供分析计算方法和参考数据。
Based on the non - Fourier heat conduction equation, the mirror method is used to consider the reflection of heat waves on the material surface. The wave propagation method is used to study the heat wave scattering problem of heterogeneous cylindrical inclusions in semi - infinite functionally graded materials. The general solution of temperature distribution in FGM is given. The effects of geometrical parameters (such as inclusion size, depth of burial) and thermophysical parameters (such as thermal conductivity and inhomogeneous parameters) on the outer surface temperature of functional graded material were analyzed. Heat waves can be excited on the material surface by means of harmonic modulation laser heating. This paper is expected to provide analytical methods and reference data for the study of non-destructive infrared thermal wave detection and thermal physics of functionally graded materials.