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<p>Considering the Volterra viscoelastic model, dynamical boundary value problems for a half-space with a cut are presented. Using the methods of contour integration and integral transforms, the problems are reduced to first kind singular integral equations with respect to jumps of the displacement component. Using the method of orthogonal polynomials, the singular integral equation is reduced to an infinite system of linear algebraic equations. The quasi-completely regularity of the obtained systems is proved, and the method of reduction for approximate solutions is developed.</p>

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Dynamic boundary value problem for the half-space under the condition of a Volterra viscoelastic model

  • 期刊论文

  • 发表日期：

    2025年7月20日

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  • Nugzar Shavlakadze,
  • Holm Altenbach

摘要

Considering the Volterra viscoelastic model, dynamical boundary value problems for a half-space with a cut are presented. Using the methods of contour integration and integral transforms, the problems are reduced to first kind singular integral equations with respect to jumps of the displacement component. Using the method of orthogonal polynomials, the singular integral equation is reduced to an infinite system of linear algebraic equations. The quasi-completely regularity of the obtained systems is proved, and the method of reduction for approximate solutions is developed.