Abstract

Background: A procedure for determining the elastic and viscous properties of the sample material on the basis of the forced vibrations of a sample of mass m loaded with a certain mass M is developed. One of advantages of using the top mass instead of a rigid fixation is the appearance of an additional deformation resonance, the frequency of which is π √ M / m times smaller than the resonance frequency of the fixed sample.

Method: The experimental setup implementing the free mass method is described. Notably, the proposed scheme does not require any adjustment and is assembled from standard devices. By changing the design of the sample only, both shear and compression-tension strains can be measured. The combination of these methods allows measuring the complex Poisson’s ratio, in addition to modulus of elasticity and loss factor.

Results: One-dimensional (1D) and two-dimensional (2D) models of specimen deformation are considered. For the 1D deformation model, approximate formulas for calculating the modulus of elasticity and the loss factor are substantiated and the limits of validity these formulas are outlined. Improving the accuracy of measurements is also considered. To do this, it is necessary to fully describe the boundary conditions on the deformable sample. The developed 2D model of sample deformation made it possible to calculate the elastic modulus form factors for various samples with axial symmetry.

Conclusion: The method may become a Standard for measuring viscoelastic properties of materials (complex elastic and shear modulus, as well as complex Poisson's ratio).