Generalized thermoelasticity based on Lord–Shulman theory that admits the second sound effect is developed for continuumbased modeling of the thermoelastic wave propagation in functionally graded material (FGM) rods with a variable crosssectional 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.

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