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Purpose <p>The study aims to present an analytical solution for the scattering of Rayleigh waves by multiple open trenches in a two-dimensional&#xa0;elastic half-plane, and to evaluate the vibration isolation effectiveness of such trench configurations.</p> Methodology <p>Based on elastodynamics theory and complex analysis, the governing equations are formulated in the complex domain, with the surface straight boundary approximated by a large circular arc. The wave function expansion method, combined with the multipolar coordinate transformation technique, is used to represent the Rayleigh wave scattering field. Conformal mapping theory is applied in conjunction with stress-free boundary conditions to derive a system of equations for the analytical solution. Parametric analyses are conducted on a double-open trench case to investigate the influence of incident wave frequency, trench depth, and trench spacing.</p> Results <p>The results indicate that multiple open trenches exhibit better vibration isolation performance than a single open trench. The incident wave frequency and trench depth are identified as the main factors affecting isolation effectiveness, while trench spacing also has a noticeable influence.</p>

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Multiple Trench Barriers for Rayleigh Wave Isolation in a 2D Elastic Ground

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Yuwang Liang,
  • Fengxi Zhou,
  • Zhixiong Zhou,
  • Xiaolin Cao

摘要

Purpose

The study aims to present an analytical solution for the scattering of Rayleigh waves by multiple open trenches in a two-dimensional elastic half-plane, and to evaluate the vibration isolation effectiveness of such trench configurations.

Methodology

Based on elastodynamics theory and complex analysis, the governing equations are formulated in the complex domain, with the surface straight boundary approximated by a large circular arc. The wave function expansion method, combined with the multipolar coordinate transformation technique, is used to represent the Rayleigh wave scattering field. Conformal mapping theory is applied in conjunction with stress-free boundary conditions to derive a system of equations for the analytical solution. Parametric analyses are conducted on a double-open trench case to investigate the influence of incident wave frequency, trench depth, and trench spacing.

Results

The results indicate that multiple open trenches exhibit better vibration isolation performance than a single open trench. The incident wave frequency and trench depth are identified as the main factors affecting isolation effectiveness, while trench spacing also has a noticeable influence.