Standing Shear Waves in Anisotropic Viscoelastic Media

We studied standing shear waves in anisotropic resonator represented by a rectangular parallelepiped (layer) fixed without slipping between two wooden plates of finite mass. The viscoelastic layer with edges of 70 mm x 40 mm x 15 mm was made of a rubber-like polymer plastisol with rubber bands inside. The bands were placed vertical between the top and the bottom plate. Mechanical properties of the plastisol itself were carefully measured previously. It was found that plastisol shows a cubic nonlinear behavior, i.e. the stress-strain curve could be represented as: sigma = mu epsilon + beta mu epsilon(3), where epsilon stands for shear strain and sigma is an applied shear stress. The value of shear modulus mu depends on frequency and was found to be several kilopascals which is common for such soft solids. Nonlinear parameter beta is frequency dependent too and varies in range from tenths to unity at 1-100 Hz frequency range, decreasing with frequency growth. Stretching the rubber bands inside the layer leads to change of elastic properties in resonator. Such effect could be noticed due to frequency response of the resonator. The numerical model of the resonator was based on finite elements method (FEM) and performed in MatLab. The resonator was cut in hundreds of right triangular prisms. Each prism was provided with viscoelastic properties of the layer except for the top prisms provided with the wooden plate properties and the prisms at the site of the rubber bands provided with the rubber properties. The boundary conditions on each prism satisfied the requirements that resonator is inseparable and all its boundaries but bottom are free. The bottom boundary was set to move horizontally with constant acceleration amplitude. It was shown numerically that the resonator shows anisotropic behavior expressed in different frequency response to oscillations applied to a bottom boundary in different directions.