Orientational instability of nematic liquid crystal under the oscillatory shear flow

The stability of the plane nematic liquid-crystal layer under the oscillatory high-frequency shear how is investigated in the case when the director is initially oriented at the angle theta(fl) = arctan(alpha(3)/alpha(2))(1/2) (where alpha(2) and alpha(3) are the viscosity coefficients) to the now direction. The approximate analytical relationships for the frequency dependence of the critical amplitude, at which theta(fl) loses stability, are derived for two limiting cases, namely, very high frequencies and relatively low shear frequencies. The data obtained are compared with the results of numerical simulation of the nematodynamic equations.