摘要
基于双曲型热传导方程,采用镜像法和波函数展开法,求解了含亚表面异质圆柱缺陷的半无限功能梯度材料的表面温度场,给出了功能梯度材料中热波散射的一般解.分析了亚表面异质圆柱缺陷的几何参数(如埋藏深度)和热物理参数(如导热系数、热扩散长度、热扩散率及热弛豫时间等)对功能梯度材料表面温度场的影响.温度波由调制的超短脉冲激光在功能梯度材料表面激发,异质圆柱缺陷表面的边界条件为导热边界.研究结果可望为功能梯度材料的红外热波无损检测、导热反问题提供计算方法和参考数据.
Inthispaper, basedonthehyperbolicequationofheatconduction, utilizingtheimagemethodandthewavefunction expansion method, the temperature distributions on the surface of a functionally graded material（FGM） containing a cylindrical inclusion are investigated. According to the model of thermal waves, a general solution of scattered fields of thermal waves is obtained. Effects of different physical parameters（such as the depth of buried inclusion, the thermal conductivity, the thermal diffusion length, the thermal diffusivity, and the thermal relaxation time） on the distribution of temperature are analyzed. The thermal waves are excited on the surface of the FGM by a periodically modulated laser. A cylindrical defect is taken as an inclusion under a thermal conduction condition. Results are expected to provide calculation methods and reference data for infrared thermal wave nondestructive evaluation of an FGM and the inverse problems in mathematical physics.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2014年第19期197-205,共9页
Acta Physica Sinica
基金
国家自然科学基金(批准号:51276129)
高超声速冲压发动机技术重点实验室基金(批准号:20130103007)资助的课题~~
关键词
功能梯度材料
双曲型热传导方程
表面温度场
异质缺陷
functionally graded material
hyperbolic equation of heat conduction
temperature distributions
cylindrical inclusion
