In the paper spatial polarizations of time-harmonic transverse plane waves propagating in micropolar elastic media are investigated along with computations of corresponding wavenumbers. This study considers the two conventional models of linear micropolar elasticity: noncentrosymmetric isotropic (also called as hemitropic) and centrosymmetric isotropic. A biquadratic algebraic equation and a 4 × 4 determinant equation for the wavenumbers k are obtained. The later is factorized and eventually reduced to single 4th degree algebraic equation. It is shown that in the case of centrosymmetric isotropy the spatial polarizations of a transverse plane wave are observed in general as a distorted polarization cross (which comprises four real polarization vectors) lying in a phase plane orthogonal to the wavevector. It is demonstrated that a transverse plane wave propagating in isotropic centrosymmetric media consists of two “individual” coupled waves of translational and spinor displacements propagating independently. For the case of noncentrosymmetric isotropy the spatial polarizations are always observed as the perfect rectangular polarization cross. Contrary to the centrosymmetric isotropy no distorted polarization crosses can be seen in a micropolar elastic medium of noncentrosymmetric isotropy.

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Polarization Crosses of Transverse Plane Waves in Micropolar Elastic Media

  • Yuri N. Radayev

摘要

In the paper spatial polarizations of time-harmonic transverse plane waves propagating in micropolar elastic media are investigated along with computations of corresponding wavenumbers. This study considers the two conventional models of linear micropolar elasticity: noncentrosymmetric isotropic (also called as hemitropic) and centrosymmetric isotropic. A biquadratic algebraic equation and a 4 × 4 determinant equation for the wavenumbers k are obtained. The later is factorized and eventually reduced to single 4th degree algebraic equation. It is shown that in the case of centrosymmetric isotropy the spatial polarizations of a transverse plane wave are observed in general as a distorted polarization cross (which comprises four real polarization vectors) lying in a phase plane orthogonal to the wavevector. It is demonstrated that a transverse plane wave propagating in isotropic centrosymmetric media consists of two “individual” coupled waves of translational and spinor displacements propagating independently. For the case of noncentrosymmetric isotropy the spatial polarizations are always observed as the perfect rectangular polarization cross. Contrary to the centrosymmetric isotropy no distorted polarization crosses can be seen in a micropolar elastic medium of noncentrosymmetric isotropy.