  The past three decades of investigation on nuclear physics and pulsar
astrophysics have seen gradual recognition that elastodynamic approach to the
continuum mechanics of nuclear matter provides proper account of macroscopic
motions of degenerate Fermi-matter constituting interior of the nuclear
material objects, the densest of all known today. This paper focuses on one
theoretical issue of this development which is concerned with oscillatory
behavior of a viscoelastic solid globe in the regime of quasistatic,
force-free, non-compressional oscillations less investigated in the literature
compared to oscillations in the regime of standing shear waves. We show that in
this case the problem of computing frequency and lifetime of spheroidal and
torsional modes of non-radial shear vibrations damped by viscosity can be
unambiguously resolved by working from the energy balance equation and taking
advantage of the Rayleigh's variational method. The efficiency of this method
is demonstrated by solid globe models of nuclear physics and pulsar
astrophysics dealing with oscillations of a spherical mass of a viscoelastic
Fermi-solid with homogeneous and non-homogeneous profiles of the bulk density,
the shear modulus, and the shear viscosity.
