Theory of acoustic resonant method for measuring the shear elasticity of liquids

The article deals with the theory of using acoustic resonance method for measuring the low-frequency shear elasticity of liquids. The acoustic resonant method is based on the application of a piezoquartz resonator which contacts with an interlayer of liquid covered with a solid cover plate. An expression for the complex shear of the resonant frequency was obtained from solving the problem of interaction in the system of a piezoelectric quartz - a liquid interlayer - a cover-plate. Taking into account that a cover-plate, due to the weak binding with the liquid interlayer, is practically at rest, we got the expressions for the real and imaginary shears of the resonant frequency and for the components of the complex phase shear in the reflection of shear wave from the boundary of liquid and cover-plate. From the analysis of the expressions for the complex shear of the resonant frequency it follows that there are two methods for measuring the shear modulus of liquids. The first method is implemented, when the liquid layer is much smaller than the length of shear wave. The second method is based on measuring the limiting values of frequency shears at a complete attenuation of the shear wave in a thick layer of liquid. We obtained the formulas for calculating the shear modulus. Both methods of measurement were experimentally implemented in this work and gave the concordant results. The experimental curves of the dependence of the frequency shears on the inverse thickness of the liquid interlayer agree well with the theoretical ones.