An interface crack with mixed electrical conditions at it faces in 1D quasicrystal with piezoelectric effect

An interface crack in 1D piezoelectric quasicrystalline space is considered. Both conducting and mixed conducting-permeable electric conditions at the crack faces are studied. The matrix-vector representations of the phonon, phason and electric quantities via the sectional-holomorphic function are derived. Two types of electrical conditions at the crack faces are considered - conducting case and mixed conducting-permeable case. A Riemann problem of linear relationship and a combined Dirichlet-Riemann boundary value problem are derived. Exact analytical solutions of the mentioned problems are presented and the simple analytical formulas for all required values are given and numerically illustrated.

Automated summary

This paper investigates the interface crack in 1D piezoelectric quasicrystalline space, studying both conducting and mixed conducting-permeable electric conditions at the crack faces, and deriving the matrix-vector representations of phonon, phason, and electric quantities. Exact solutions are presented for the Riemann problem of linear relationship and the combined Dirichlet-Riemann boundary value problem, with simple analytical formulas for all required values given and numerically illustrated.