Surface and interfacial waves in anisotropic elastic quasicrystals

•Stroh formalism for two-dimensional subsonic motion of anisotropic quasicrystals.•At most three subsonic surface wave speeds in anisotropic quasicrystals.•At most one surface wave in half-space for a traction-free and insulating surface.•At most two subsonic surface wave speeds for a traction-free and conducting surface

We present the Stroh formalism for two-dimensional subsonic steady-state motion of anisotropic quasicrystals. Using this new formalism and a series of identities and properties which follow, we investigate subsonic surface and interfacial waves in anisotropic quasicrystals. Our results suggest that there exist at most three subsonic surface wave speeds. This interesting observation is quite different from the unique surface wave speed known for anisotropic crystals. The degenerate case of decagonal quasicrystalline materials is discussed in detail.