Generalized Poro-thermoelastic Waves in the Cylindrical Plate Framed with Liquid Layers

PurposeThe examination of the behavior of wave propagation through different kinds of materials under various mathematical models certainly brings out new properties of those materials to the fore. In this contribution, the circular-crested Lamb-type waves in an isotropic homogeneous, elasto-thermal plate with voids sandwich-packed by inviscid liquid layers have been examined in the context of Lord-Shulman and Green-Lindsay generalizations.MethodsHelmholtz's decomposition principle has been used to separate the solenoidal part and the lamellar part of the waves. The normal mode analysis technique has been used to obtain solutions to governing equations. With the help of solutions, the obtained partial differential equations have been converted to ordinary differential equations to find the eigenvalues of the elasto-porothermal plate bordered with inviscid liquid layers. The problem has also been solved from a numerical point of view and the results have been portrayed graphically.ResultsThe transverse horizontal wave being unaltered due to voids and temperature gradient gets separated from the coupled system corresponding to elastic waves (compressional and transverse vertical), thermal waves, and wave motion due to voids. Apart from that, each layer of liquid possesses one longitudinal wave. The frequency equations have been derived for the flexural and longitudinal wave modes by solving the stiffness matrix. The inviscid fluid and voids decrease the magnitude of phase velocity and attenuation coefficient. Thermal relaxation times have a small impact on wave propagation.ConclusionsThe problem of circular-crested Lamb-type waves has been solved mathematically which lays a theoretical foundation for further study of Lamb-type wave propagation in plates. The present work may find applications in many fields such as the petroleum industry, earthquake engineering, soil dynamics, hydrology, as well as biomechanics.

Automated summary

In this study, the propagation behavior of circular-crested Lamb-type waves in an isotropic homogeneous plate with inviscid liquid layers was examined. The solenoidal and lamellar parts of the waves were separated using Helmholtz's decomposition principle, and the governing equations were solved using the normal mode analysis technique. The presence of inviscid fluid layers and voids was found to decrease the phase velocity and attenuation coefficient of the waves.