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Fundamental solutions and frictionless contact problem in a semi‐infinite space of 2D hexagonal piezoelectric QCs
Author(s) -
Li Caiqi,
Zhou YueTing
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800132
Subject(s) - phason , superposition principle , conical surface , piezoelectricity , mathematical analysis , field (mathematics) , classical mechanics , space (punctuation) , mathematics , physics , geometry , quasicrystal , pure mathematics , computer science , acoustics , operating system
General solutions for the semi‐infinite space of two‐dimensional (2D) piezoelectric quasicrystals (QCs) are acquired by means of the potential theory method and the generalized Almansi's theorem. Then based on the fundamental solutions of the concentrated loadings case, the frictionless contact problem in a semi‐infinite of 2D hexagonal piezoelectric QCs is addressed by using the superposition principle and potential theory. Analytic solutions of fields quantities in terms of elementary functions for the phonon field, phason field and electric field are obtained under three different rigid indenters (flat‐ended cylindrical, conical and spherical), which are convenient for numerical analysis. Numerical examples are given to display the relationship between the contact stiffness and the penetration depth through the change of the curves, and to demonstrate the distribution of the field components under the action of the flat‐ended cylindrical.