The present work devotes to investigating the transient responses of a half-space with variable thermal material properties based on the generalized thermoelastic theory with memory-dependent derivative. The bounding surface is assumed to be traction free and heated by a non-Gaussian laser beam. The material characteristic parameters are assumed as the linear function of temperature. The coupled governing equations containing thermal time-delay factor and kernel function, which can be chosen to adapt to specific problems, are formulated and solved by the Laplace and Kirchhoff transformations. Numerical results of the non-dimensional temperature, displacement as well as stress under different time, variable thermal conductivity, thermal time-delay factor and kernel function are obtained and illustrated graphically. It is hoped that the obtained results would be helpful in designing the temperature-dependent structures heated by a non-Gaussian laser beam in engineering.

目前的工作致力于基于具有记忆相关导数的广义热弹性理论研究具有可变热材料特性的半空间的瞬态响应。边界表面被假定为无牵引并由非高斯激光束加热。材料特性参数被假定为温度的线性函数。通过拉普拉斯和基尔霍夫变换制定和求解包含热时延因子和核函数的耦合控制方程，可以选择以适应特定问题。得到了无量纲温度、位移和不同时间应力、变热导率、热延时因子和核函数的数值结果，并以图形方式说明。