<p>This paper investigates the reflection and transmission of qP waves through a nonlocal orthotropic layer sandwiched between two nonlocal orthotropic half-spaces in welded contact using the weakly nonlocal model of elasticity. Different from other existing nonlocal models, this theory has been proven well-posed for any harmonic plane wave problem. The main aim of this study is to find explicit expressions for the reflection and transmission coefficients. By using the surface impedance matrix method and the effective boundary condition method, explicit expressions for the reflection and transmission coefficients have been derived. In particular, to find the reflection coefficients, we replace the entire effect of the layer and the transmission half-space on the reflection half-space by effective boundary conditions at the surface of the reflection half-space. Then, the reflection coefficients have been derived without finding the wave fields in the layer and the transmission half-space. Analogously, replacing the entire effect of the layer and the reflection half-space by effective boundary conditions at the surface of the transmission half-space, the transmission coefficients are also derived. Some numerical examples carried out to show the effect of the thickness of layer, the nonlocality and the incident angle on the reflection and transmission coefficients. Since the obtained formulas are totally explicit, they are very significant in various practical applications.</p>

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Reflection and transmission of qP waves through a nonlocal orthotropic layer sandwiched between two nonlocal orthotropic half-spaces

  • P. C. Vinh,
  • T. T. Tuan,
  • V. T. N. Anh

摘要

This paper investigates the reflection and transmission of qP waves through a nonlocal orthotropic layer sandwiched between two nonlocal orthotropic half-spaces in welded contact using the weakly nonlocal model of elasticity. Different from other existing nonlocal models, this theory has been proven well-posed for any harmonic plane wave problem. The main aim of this study is to find explicit expressions for the reflection and transmission coefficients. By using the surface impedance matrix method and the effective boundary condition method, explicit expressions for the reflection and transmission coefficients have been derived. In particular, to find the reflection coefficients, we replace the entire effect of the layer and the transmission half-space on the reflection half-space by effective boundary conditions at the surface of the reflection half-space. Then, the reflection coefficients have been derived without finding the wave fields in the layer and the transmission half-space. Analogously, replacing the entire effect of the layer and the reflection half-space by effective boundary conditions at the surface of the transmission half-space, the transmission coefficients are also derived. Some numerical examples carried out to show the effect of the thickness of layer, the nonlocality and the incident angle on the reflection and transmission coefficients. Since the obtained formulas are totally explicit, they are very significant in various practical applications.