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<p>The problem of Rayleigh waves propagating in Eringen’s (integral) nonlocal piezoelectric half-spaces has been investigated (Thin-Walled Structures 208 (2025), 112765; Vietnam Journal of Mechanics 41 (2019), 363–371). However, since the authors employed the non-equivalent differential nonlocal model, which lacks the constitutive boundary conditions and the Eringen method, which does not satisfy the original equations of motion, the obtained solution is not the desired one. The main aim of this paper is to reconsider this problem. The problem is first reformulated using the equivalent differential nonlocal piezoelectricity model that includes the constitutive boundary conditions. Then, the well-posedness of the problem is examined using a recently established criterion (Proc. R. Soc. A 480 (2293) 20230814, 2024). Finally, its solution is derived using a novel method (Proc. R. Soc. A 480 (2293) 20230814, 2024) that satisfies the constitutive boundary conditions and the original equations of motion. The solution provides the expressions for displacements, electric potential, stresses, electric displacements as well as the dispersion equation and the H/V ratio. Numerical results demonstrate that the nonlocality decreases the Rayleigh wave velocity and increases the H/V ratio, while the piezoelectricity increases both the Rayleigh wave velocity and the H/V ratio.</p>

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Nonlocal piezoelectric Rayleigh waves satisfying constitutive boundary conditions and original equations of motion

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Le Thi Hue,
  • Pham Chi Vinh,
  • Tran Thanh Tuan,
  • Vu Thi Ngoc Anh

摘要

The problem of Rayleigh waves propagating in Eringen’s (integral) nonlocal piezoelectric half-spaces has been investigated (Thin-Walled Structures 208 (2025), 112765; Vietnam Journal of Mechanics 41 (2019), 363–371). However, since the authors employed the non-equivalent differential nonlocal model, which lacks the constitutive boundary conditions and the Eringen method, which does not satisfy the original equations of motion, the obtained solution is not the desired one. The main aim of this paper is to reconsider this problem. The problem is first reformulated using the equivalent differential nonlocal piezoelectricity model that includes the constitutive boundary conditions. Then, the well-posedness of the problem is examined using a recently established criterion (Proc. R. Soc. A 480 (2293) 20230814, 2024). Finally, its solution is derived using a novel method (Proc. R. Soc. A 480 (2293) 20230814, 2024) that satisfies the constitutive boundary conditions and the original equations of motion. The solution provides the expressions for displacements, electric potential, stresses, electric displacements as well as the dispersion equation and the H/V ratio. Numerical results demonstrate that the nonlocality decreases the Rayleigh wave velocity and increases the H/V ratio, while the piezoelectricity increases both the Rayleigh wave velocity and the H/V ratio.