High-Frequency Inertia Anisotropic Mode

to date we have three theoretically predicted modes for a high-frequency instability caused by the Carr-Helfrich anisotropic mechanism. They are the conductance and dielectric regimes and the inertia mode. Two of these (the conducting regime and the inertia mode) correspond to the steady-state motion of the liquid and the stationary deviations of the 

The only serious discrepancy between experiment [44, 93, 94] and theory [92] is the geometry of the flows. Theoretically, at least close to the threshold, the flow of the liquid and the distortion of the director should occur in the xz-plane (Fig. 5.11). However, optical observations show that the fiow and distortion occur in the xy-plane of the layer. It is possible, however, that in the experiment we are dealing with the situation occurring slightly above the threshold, whereas the theory only predicts the situation just at the threshold. This topic requires further investigation. 

Meanwhile, investigations of wide domains have identified the causes of chevron, herring-bone structures. These result fi om interference between two modes with neighboring thresholds— the linear prechevron domains (deformation in the xz-plane) and the wide domains (deformation in the xy-plane). It has also proved possible to obtain such a herringbone structure by 

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As mentioned above, when the transverse dimensions of the beam are of the same order of magnitude as the length, the simple beam theory must be corrected to introduce the effects of the shear stresses, deformations, and rotary inertia. The theory becomes inadequate for the high frequency modes and for highly anisotropic materials, where large errors can be produced by neglecting shear deformations. This problem was addressed by Timoshenko et al. (7) for the elastic case starting from the balance equations of the respective moments and transverse forces on a beam element. Here the main lines of Timoshenko et al. s approach are followed to solve the viscoelastic counterpart problem. 

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