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<p>This article proposes an analytical solution of the magneto-elastic coupling effect on the dispersion of longitudinal waves in a&#xa0;magnetize isotropic elastic solid containing three co-linear cracks. The dispersion effect of three co-linear Griffith cracks located in a&#xa0;homogeneous infinite isotropic medium due to the influence of magnetic field is formulated as a&#xa0;mixed boundary value problem (MBVP). The MBVP have been transformed to a&#xa0;set of integral equations introducing Abel’s transform which have further been simplified using perturbation method for low frequency by concerning the iterative expansion of Bessel’s and Hankel’s functions. The converted integral equations have been solved by Hilbert transformation and Cooke Results. The semi-analytical expressions of crack opening displacement and stress intensity factors have been derived related to low frequency waves. Numerical outcomes of crack opening displacement and stress intensity factors for several crack lengths with the presence of magnetic field have been computed and presented graphically to exhibit the influence of magnetization. Some special cases have been discussed.</p>

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Dispersion of longitudinal waves by three co-linear Griffith cracks in a magnetized elastic medium

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Ujjal Dhabal,
  • Subhadeep Naskar,
  • S. C. Mandal

摘要

This article proposes an analytical solution of the magneto-elastic coupling effect on the dispersion of longitudinal waves in a magnetize isotropic elastic solid containing three co-linear cracks. The dispersion effect of three co-linear Griffith cracks located in a homogeneous infinite isotropic medium due to the influence of magnetic field is formulated as a mixed boundary value problem (MBVP). The MBVP have been transformed to a set of integral equations introducing Abel’s transform which have further been simplified using perturbation method for low frequency by concerning the iterative expansion of Bessel’s and Hankel’s functions. The converted integral equations have been solved by Hilbert transformation and Cooke Results. The semi-analytical expressions of crack opening displacement and stress intensity factors have been derived related to low frequency waves. Numerical outcomes of crack opening displacement and stress intensity factors for several crack lengths with the presence of magnetic field have been computed and presented graphically to exhibit the influence of magnetization. Some special cases have been discussed.