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Magnetically Induced Rotating Rayleigh-Taylor Instability
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On non-locally elastic Rayleigh wave.

J Kaplunov1, D A Prikazchikov1, L Prikazchikova1

  • 1School of Computer Science and Mathematics, Keele University, Keele ST5 5BG, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|July 20, 2022
PubMed
Summary
This summary is machine-generated.

A revised differential model for non-local elasticity accurately describes Rayleigh-type waves, incorporating a non-local boundary layer. This model corrects the classical Rayleigh wave speed, enhancing wave propagation analysis in complex media.

Keywords:
boundary layerdiscrete chainintegral and differential modelsnon-local elasticitysurface wave

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Area of Science:

  • Solid Mechanics
  • Continuum Mechanics
  • Wave Propagation

Background:

  • The differential formulation of non-local elasticity is widely used for wave analysis.
  • Existing models may not fully capture the nuances of non-local stress interactions.
  • Rayleigh-type waves are crucial for understanding surface wave phenomena.

Purpose of the Study:

  • To revisit and critically evaluate the existing Rayleigh-type wave solution in differential non-local elasticity.
  • To develop a modified differential model that incorporates a non-local boundary layer.
  • To establish the correspondence between the modified model and the integral theory of non-local elasticity.

Main Methods:

  • Revisiting the established Rayleigh-type wave solution within the differential formulation.
  • Developing a modified differential model by introducing a non-local boundary layer.
  • Analyzing the asymptotic behavior of the modified model and its correspondence to integral theory using a Bessel function kernel.
  • Investigating a toy problem for a semi-infinite chain to assess the continuous setup for boundary layer modeling.

Main Results:

  • The widely used Rayleigh-type wave solution in differential non-local elasticity was found to be inconsistent with the equations of motion for non-local stresses.
  • A novel modified differential model was developed, successfully incorporating a non-local boundary layer.
  • The modified model shows correspondence with the integral theory, yielding a leading-order non-local correction to the classical Rayleigh wave speed due to boundary layer effects.

Conclusions:

  • The developed modified differential model provides a more accurate description of Rayleigh-type wave propagation in non-local elasticity.
  • The inclusion of a non-local boundary layer is essential for capturing the correct wave behavior and speed.
  • The study validates the suitability of continuous models for analyzing boundary layers within non-local elasticity frameworks.