  Within the framework of Newtonian magneto-solid-mechanics, relying on
equations appropriate for a perfectly conducting elastic continuous medium
threaded by a uniform magnetic field, the asteroseismic model of a neutron star
undergoing axisymmetric global torsional nodeless vibrations under the combined
action of Hooke's elastic and Lorentz magnetic forces is considered with
emphasis on a toroidal Alfv\'en mode of differentially rotational vibrations
about the dipole magnetic moment axis of the star. The obtained spectral
equation for frequency is applied to $\ell$-pole identification of
quasi-periodic oscillations (QPOs) of X-ray flux during the giant flares of SGR
1806-20 and SGR 1900+14. Our calculations suggest that detected QPOs can be
consistently interpreted, within the framework of this model, as produced by
global torsional nodeless vibrations of quaking magnetar if they are considered
to be restored by the joint action of bulk forces of shear elastic and magnetic
field stresses.
