Orientational instability of nematic liquid crystal under the oscillatory shear flow

The stability of the plane nematic liquid-crystal layer under the oscillato ry high-frequency shear how is investigated in the case when the director i s 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 d irection. The approximate analytical relationships for the frequency depend ence of the critical amplitude, at which theta(fl) loses stability, are der ived for two limiting cases, namely, very high frequencies and relatively l ow shear frequencies. The data obtained are compared with the results of nu merical simulation of the nematodynamic equations.