Beschreibung:
<jats:title>Abstract</jats:title><jats:p>Despite the widespread application of mechanical waves in solidifying metals, the wave propagation laws in melt and the motion patterns of melts are unclear, which has seriously hindered the development of vibration solidification treatment. It is difficult to solve the wave propagation because of the spatial heterogeneity and the intrinsic viscoelasticity of solidifying metals. In this paper, a physico‐mathematical model is developed by coupling the unsteady temperature field and the integral Hooke–Kelvin model unifying various rheological models during solidification, and simplifies to wave equations by introducing memory factors. Then, the wave equations are solved by a staggered‐grid high‐order difference method. Subsequently, the propagation laws of mechanical waves in a large casting and a feeding channel during solidification are analyzed, eventually verified by casting experiments. It is shown that the viscoelasticity of solidifying metals is significant for the wave field. In the large casting, both displacements and stresses exhibit complex multi‐lobe patterns. In the feeding channel, the formation of micropores between the quasi‐liquid and the quasi‐solid phase and the feeding improvement by vibrations are well explained by simulation. The numerical model is a novel reliable method to theorize the solidification under vibration and expands the potential applications of vibration.</jats:p>