Indirect assessment of bulk strain soliton velocity in opaque solids

Abstract

This paper presents a methodology allowing for determination of strain soliton velocity in opaque solid materials. The methodology is based on the analysis of soliton evolution in a layer of a transparent material adhesively bonded to the layer of a material under study. It is shown that the resulting soliton velocity in the complex waveguide equals to the arithmetic mean of soliton velocities in the two component materials. The suggested methodology is best suited for analysis of materials with relatively close elastic parameters and can be applied in research of nonlinear wave processes in opaque composites on the basis of transparent matrices.

Polystyrene-Based Nanocomposites with Different Fillers: Fabrication and Mechanical Properties

“…The nanocomposite layers and those of fabricated PS samples were made by bonding the corresponding plates with the ethylcyanoacrylate Superglue adhesive. As we have demonstrated previously [43,44], elastic features of this adhesive are close to those of the applied polymers and it does not affect noticeably the soliton behavior.…”

“…As shown in [42], in a layered bar made of two different materials a single soliton is formed, the amplitude and width of which depend upon elastic properties of the corresponding materials. As shown in [43] the soliton velocity measured in such a sandwich waveguide in one of the layers equals the arithmetic mean of soliton velocities in waveguides of the same geometry but made of each of the materials.…”

“…Note that the reported holographic arrangement operates with transparent specimens only. To perform wave detection in opaque materials, as all composites are, we recently suggested an approach allowing for indirect recording of strain waves in opaque materials by monitoring phase shift gradients in a layer of transparent material adhesively bonded to the layer made of the material of interest [42,43]. As shown in [42], in a layered bar made of two different materials a single soliton is formed, the amplitude and width of which depend upon elastic properties of the corresponding materials.…”

On Boussinesq-type models for long longitudinal waves in elastic rods

“…Here, all four models have the same nonlinear terms, but they have different dispersive terms. Equations (46) and (47) can also be written in the form of the equation (45) with the following dispersive coefficients, respectively:…”

“…for the equations (45), (46) and (47) respectively. In the left part of the Figure 3 we plot the four solitons given by the formulae (82) -(85) for one and the same value of the amplitude parameter A = −0.05 and the same elastic moduli shown in Table 1 (typical for a polystyrene [35]).…”