Generalized thermoelasticity based on Lord–Shulman theory that admits the second sound effect is developed for continuum-based modeling of the thermoelastic wave propagation in functionally graded material (FGM) rods with a variable cross-sectional area under quadratic thermal shock loading. The geometry of the problem, as well as the distribution of material properties, is defined continuously with Non-uniform rational B-spline. To assure the exact modeling of geometry, the problem is analyzed using the isogeometric approach. The effects of geometry and material distribution on thermoelastic waves are discussed in detail. Also, propagation, reflections, and propagation speed along the rod axis are investigated. It is shown that the amplitudes and speed of thermoelastic waves can be desirably controlled by the cross-sectional area and the material distribution of the rod, respectively.

中文翻译：

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二次热冲击载荷下非均匀有理B样条杆中的广义热弹性波传播使用等几何方法

广义热弹性基于 Lord-Shulman 理论，该理论承认第二种声音效应，用于对二次热冲击载荷下具有可变横截面积的功能梯度材料 (FGM) 棒中的热弹性波传播进行基于连续介质的建模。问题的几何形状以及材料属性的分布是用非均匀有理 B 样条连续定义的。为了确保几何的精确建模，使用等几何方法来分析问题。详细讨论了几何形状和材料分布对热弹性波的影响。此外，还研究了沿杆轴的传播、反射和传播速度。