Scattering of flexural waves in mindlin's plates of soft ferromagnetic materials with a cutout

The problem of elastic waveguide and dynamic stressconcentrations in plates with a cutout is the important subject in solidmechanics. The cutout in structures has influence directly on the loadingcapacity and the lifetime of structures, therefore, some researchers havedevoted to theoretical analysis and experimental research in the world.Considered dynamic stress concentration or intensity factors, the classicaltheory of thin plate has disadvantage. Thick plate theory proposed byMindlin made up for the shortage classical theory of thin plate includingthe effect of transverse shear deformation and rotator inertia. Thesatisfying result is gained in engineering. In the 1960's, with wavefunction expansion method, Pao Yih-Hsing first studied the problem of theflexural wave scattering and dynamic stress concentrations in Mindlin'sthick plates with circular cavity and gave an analytical solution andnumerical results.With the development of modern science and technology, the ferromagneticmaterials have been applied to superconduct nuclear power station andmagnetic levitation trains. It has better physical and mechanical property.The stress on the contour of a cavity or crack in ferromagnetic materialsmay be increase in a uniform magnetic field. It has a influence on thecarrying capacity and the lifetime of structures. According to the manyreferences, the dynamical behavior of ferromagnetic elastic structures canbe significantly affected by the presence of a uniform magneticfield.Based on the theory of magneto-elastic interaction, Japaneseresearchers analyzed scattering of flexural wave and the dynamic bendingmoment intensity factors in cracked Mindlin plates of ferromagneticmaterials and gave numerical results. They used Fourier transforms to reducethe mixed boundary value problem to a Fredholm integral equation that can besolved numerically.In this paper, based on the equation of wave motion in Mindlin's plate ofmagneto-elastic interaction, using wave function expansion method, thescattering of flexural wave and dynamic stress concentrations in a plate offerromagnetic materials with a cutout are investigated. According toanalysis and numerical results, the magnetic induction intensity has greatinfluence on the dynamic stress concentration factors at low frequency.