Viscoelastic Nonlinear Resonator with Gas-Filled Cavities

We studied shear waves of finite amplitude in a resonator in the form of a rectangular parallelepiped made of viscoelastic material with gas-filled through cavities on the side surface. The cavities are parallel to the parallelepiped bases and perpendicular to the oscillations direction. The centers of the cavities are displaced to one of the bases, allowing us to investigate two different configurations of resonator with cavities near the top and near the bottom base. The equation of motion of particles in the resonator was obtained using a model of a medium with a single relaxation time and cubic dependence of the shear modulus on deformation. The amplitude and shape of the shear waves in the resonator were numerically calculated, applying the finite differences method for the shifted grids. Measurements were carried out in a resonator in the form of a rectangular 15-mm thick parallelepiped made of a viscoelastic polymer plastisol. There were six through cavities with a square cross-section with 5 mm sides. The amplitude of oscillations at the first resonance frequency was sufficient to observe nonlinear effects. It was shown that nonlinear effects are more pronounced in the resonator with cavities located in the region of maximal deformation.