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Mathematical modelling of the electromagnetic type transducers in the excitation mode of the ultrasonic waves. (Ukrainian. English summary) Zbl 1413.74050

Summary: A mathematical model of an electromagnetic-type electroacoustic transducer is determined in the excitation (radiation) mode of ultrasonic waves in metals. A boundary value problem of dynamic magnetoelaslicity is formulated, which takes into account not only the ponderomotive effect of the electromagnetic field on the metal sample, but also the existence of magnetostriction effects in metals of the ferromagnetic group. The solution of this problem makes possible to preserve the coupling effect of the elastic and magnetic fields in the volume of a deformable ferromagnet, that manifests itself in an increase of the metal elastic moduli (\(\Delta E\)-effect). To solve the dynamic magnetoelastic problem, the method of successive approximations is proposed, which basically has the assumption that the \(\Delta E\)-effect is small (less than 20%). It is shown that zero approximation to the exact value of the displacement vector components of the ferromagnet material particles allows to preserve in the solutions information about the design and geometric parameters of the alternating magnetic field source. The first approximation gives corrections that somewhat decrease the amplitude values of the displacement vector components of the metal material particles. This is equivalent to taking into account the \(\Delta E\)-effect. Moreover, the error in determining the displacement vector components does not exceed the fourth degree of the magnetomechanical coupling coefficient.

MSC:

74F15 Electromagnetic effects in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
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