Fundamental solutions of critical wedge angles for one-dimensional piezoelectric quasicrystal wedge

• Published in: Applied mathematics and mechanics Vol. 43; no. 5; pp. 709 - 728
• Main Authors: Mu, Xiang, Fu, Xiaoyu, Zhang, Liangliang, Zhu, Zhaowei, Zhang, Jinming, Gao, Yang
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.05.2022; College of Science,China Agricultural University,Beijing 100083,China; College of Engineering,China Agricultural University,Beijing 100083,China%College of Science,China Agricultural University,Beijing 100083,China
• Subjects: Applications of Mathematics; Classical Mechanics; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; quasicrystal (QC); 74A60; piezoelectric effect; 52C23; wedge; critical angle; analytical solution; O343.7; 82D80; quasicrystal(QC)
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-022-2847-6

Two problems of a one-dimensional (1D) piezoelectric quasicrystal (QC) wedge are investigated, i.e., the two sides of the wedge subject to uniform tractions and the wedge apex subject to the concentrated force. By virtue of the Stroh formalism and Barnett-Lothe matrices, the analytical expressions of the displacements and stresses are derived, and the generalized solutions for the critical wedge angles are discussed. Numerical examples are given to present the mechanical behaviors of the wedge in each field. The results indicate that the effects of the uniform tractions and the concentrated force on the phonon field displacement are larger than those on the phason field.