ИСТИНА

Measurements of the nonlinear parameter of a gel-like medium were carried out by static and dynamic methods in an acoustical resonator in the form of a rectangular parallelepiped fixed without slipping between two solid-state boundaries. The standing shear wave excitation method is illustrated in fig. 1. A sample of thickness L is fixed on an oscillating plate (x = 0). Plate of finite mass on the free surface (x = L) moves together with this surface. Metal weights are attached to the oscillating plate. By changing the number of weights, it is possible to achieve additional static deformation of the resonator up to 65%. It has been shown [1] that a one-dimensional model can be applied to a resonator if its length in the direction of oscillations is 4 or more times greater than its thickness. The resonator is made of plastisol, a gel-like polymer material. Layer is solidified in a rectangular shape between two parallel wooden plates. Rods are attached to one of the plates for the weights to be placed in order to create a static deformation of the resonator. The developed dynamic method for measuring a nonlinear parameter assumes measuring resonance curves at various static deformations. The resonance curves show the ratio of the acceleration amplitudes of the resonator plates. The effective shear modulus of the material for a given resonator load depends on the resonance frequency. Dots on fig. 2 represent the experimental dependence of the effective shear modulus on the relative deformation created by the static load. In the dynamic method, nonlinear properties appear at strains of more than 20%. According to this dependence, the nonlinear parameter 𝛽 = 0.53 ± 0.06 was determined by the method of approximation with a quadratic polynomial (solid line). Shear modulus measured dynamically: 𝜇 = 15.4 ± 1.1 kPa. The results were compared to static measurements where static shear stress was applied to the resonator and its dependence on the relative deformation of the resonator was plotted. At strains greater than 30%, the dependence becomes nonlinear. Approximation by a cubic polynomial makes it possible to determine the nonlinear parameter. The shear modulus 𝜇 = 13.46 ± 0.13 kPa and the nonlinear parameter 𝛽 = 0.60 ± 0.07 were obtained. As a result, a method based on measuring resonance curves at low amplitudes with an applied static shear stress that creates nonlinear deformation was developed for measuring the linear shear modulus and the nonlinear parameter of a gel-like material. The nonlinear parameter obtained by this method coincided with the nonlinear parameter measured statically within the error. It was found that when measured by the dynamic method, the nonlinear properties of the material appear at lower strains than when measured by the static method. At a static deformation of more than 20%, the nonlinearity of the shear modulus of plastisol appears, which leads to an increase in the resonance frequency in comparison with the absolutely linear case [2]. This effect is common for plastisol [3]. From the dependence of the effective shear modulus on the deformation, the nonlinear parameter 𝛽 was detrmined. ACKNOWLEDGEMENTS This work is supported by RSCF, project No. 22-22-00751.