Abstract：As an advanced material, quasicrystal (QC) exhibits distinctive physical characteristics including high hardness, a low friction coefficient, and exceptional wear resistance that make them promising for multifunctional structural applications. Despite substantial progress in understanding the intrinsic properties of QC materials, their mechanical behavior when incorporated into complex structural systems remains insufficiently understood. In particular, the response mechanisms of QC structures under multi-field coupling conditions have not yet been fully clarified. Among these challenges, the mechanical performance of QC laminated beams interacting with elastic media remains an underexplored problem. This paper investigates the buckling, vibration, and bending of simply-supported one-dimensional (1D) hexagonal QC layered beams interacting with an elastic medium. The model is formulated using the pseudo-Stroh formulation combined with the transfer matrix method. The general solution is derived for the critical buckling load, natural frequencies, bending deflection, and stresses under two typical elastic medium configurations: beams embedded in the medium and beams resting on it. The accuracy of the model is validated by comparing results with existing studies. Numerical examples systematically examine the effects of the slenderness ratio, stacking sequence, and elastic-medium parameters on the mechanical responses. The results show that simply-supported 1D hexagonal QC layered beams embedded in the elastic medium exhibit higher natural frequencies and critical buckling loads than those resting on it. Stacking sequences with higher elastic constants in the outer layers significantly improve structural performance. Both Winkler stiffness KW and shear modulus KG enhance the frequency and buckling capacity, with KW having a stronger influence due to its direct relation to displacement. Structural symmetry determines the mode shapes: symmetric distributions occur for beams embedded in or without elastic media, while beams on the medium show asymmetry. This study provides exact analytical solutions and design insights for QC layered beams in elastic media, offering a theoretical foundation for further numerical and experimental research in aerospace, mechanical, and composite engineering.
2026, Vol. 47 
