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The past three decades of investigation on nuclear physics and pulsarastrophysics have seen gradual recognition that elastodynamic approach to thecontinuum mechanics of nuclear matter provides proper account of macroscopicmotions of degenerate Fermi-matter constituting interior of the nuclearmaterial objects, the densest of all known today. This paper focuses on onetheoretical issue of this development which is concerned with oscillatorybehavior of a viscoelastic solid globe in the regime of quasistatic,force-free, non-compressional oscillations less investigated in the literaturecompared to oscillations in the regime of standing shear waves. We show that inthis case the problem of computing frequency and lifetime of spheroidal andtorsional modes of non-radial shear vibrations damped by viscosity can beunambiguously resolved by working from the energy balance equation and takingadvantage of the Rayleigh's variational method. The efficiency of this methodis demonstrated by solid globe models of nuclear physics and pulsarastrophysics dealing with oscillations of a spherical mass of a viscoelasticFermi-solid with homogeneous and non-homogeneous profiles of the bulk density,the shear modulus, and the shear viscosity.

Spheroidal and torsional modes of quasistatic shear oscillations in the solid globe models of nuclear physics and pulsar astrophysics