Stress relaxation and thermo-visco-elastic effects in fluid-filled slits and fluid-loaded plates

Abstract

In this paper, we theoretically analyse wave propagation in two canonical problems of interest: fluid-filled thermo-visco-elastic slits and fluid-loaded thermo-visco-elastic plates. We show that these two configurations can be studied via the same pair of dispersion equations with the aid of the framework developed in García Neefjes et al. (2022), which incorporates thermal effects. These two problems are further interrelated, since in the short wavelength limit (relative to the slit/plate width) the respective modes are governed by the same dispersion equation, commonly known as the Scholte–Stoneley equation. It is the Scholte-type modes that are mainly analysed in this paper. We illustrate results when the fluid is water, although the theory is valid for any Newtonian fluid. Both ‘hard’ and ‘soft’ solids are compared, with the emphasis being placed on the importance of thermo-viscoelastic effects, particularly when stress relaxation is considered. Two main recent works are discussed extensively, namely (Cotterill et al., 2018) for slits and (Staples et al., 2021) for loaded plates, both of which do not incorporate viscoelastic mechanisms. We show how the consideration of viscoelasticity can extend the results discussed therein, and explain the circumstances under which they arise.