The nonlinear dynamic equations introduced by Biot to model porous media have not been implemented to describe nonlinear acoustic waves in such media. In this work the equations are revised and a mathematical model depicting the physical nonlinearity is established. A perturbation technique is then applied to find solutions to the nonlinear Biot equations. An important feature of the developed model is the introduction of the dependence of the structural parameters of the medium on its porosity. The model establishes a correlation between the measurable effective nonlinear parameter and structural parameters of the porous medium. This suggests employing nonlinear measurements as a diagnostic tool for porous media.
The nonlinear dynamic equations introduced by Biot to model poroelastic media have not been implemented to describe nonlinear acoustic waves in such media. The equations of the semilinear Biot model are revised and a mathematical model depicting the physical nonlinearity is established. A perturbation technique is then applied to find solutions to the nonlinear Biot equations. The computational results are carried out in details for a one-dimensional model in which the contributions of the fast and slow compressional waves into second harmonic wave are analyzed. The correlation between second and third-order Biot coefficients and measurable nonlinear parameters is also presented along with a parameter analysis.
The linear acoustic equations for the bounded slab of fluid ocean and elastic seabed with cylinderical symmetry are reduced to a set of coupled boundary value problems using separation of variables. In order to have a computational technique capable of handling stratification effects in the seabed, invariant imbedding is used to replace the boundary value problem with an initial value problem. As an initial approximation, the case of an ocean with a reflective bottom is considered and the change in the solution, as the depth of the seabed increases, is calculated. The method of invariant imbedding is shown to be numerically stable and has the advantage of assessing the effects of including an interactive seabed on the solution to the underwater acoustics problem with a reflecting seabed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.