On the interfacial behavior of a one-dimensional hexagonal piezoelectric quasicrystal film based on the beam theory

doi:10.1007/s10483-025-3214-9

Abstract

Abstract:

In this paper, the mechanical response of a one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) thin film is analyzed under electric and temperature loads. Based on the Euler-Bernoulli beam theory, a theoretical model is proposed, resulting in coupled governing integral equations that account for interfacial normal and shear stresses. To numerically solve these integral equations, an expansion method using orthogonal Chebyshev polynomials is employed. The results provide insights into the interfacial stresses, axial force, as well as axial and vertical deformations of the PQC film. Additionally, fracture criteria, including stress intensity factors, mode angles, and the J-integral, are evaluated. The solution is compared with the membrane theory, neglecting the normal stress and bending deformation. Finally, the effects of stiffness and aspect ratio on the PQC film are thoroughly discussed. This study serves as a valuable guide for controlling the mechanical response and conducting safety assessments of PQC film systems.

Key words: one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) film, beam theory, electric and temperature loads, Chebyshev polynomial, interfacial behavior

2010 MSC Number:

O343.1

Wenkai ZHANG, C. S. LU, Minghao ZHAO, Cuiying FAN, Huayang DANG. On the interfacial behavior of a one-dimensional hexagonal piezoelectric quasicrystal film based on the beam theory. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 289-304.

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