Mathematical models of dynamic systems that include layered watered poroelastic foundations
https://doi.org/10.12737/20215
Abstract
New mathematical models including an oscillation generator and semi-bounded non-uniform in depth foundation possessing porosity, fluid saturation, and viscoelasticity, are considered. The foundation is represented by a poroelastic layer saturated with gas-liquid mixture, a heterogeneous layer with a viscoelastic coating, and a heterogeneous layer with a subsurface liquid sheet. The foundation of the pack of layers is hard. The operation of the surface oscillator is represented as Fourier series, and the problem of steady-state oscillatory conditions is solved. Applying the Fourier integral transform to the equations that describe continuous media under satisfying boundary conditions allows the construction of integral formulas describing the stress-strain condition in the layer package. A numerical algorithm to study the dependence of the ground-wave propagation on the mechanical and geometrical characteristics of the problem is proposed. The models described are widely used in Geophysics, seismic exploration, construction, railway design, and new material designing.
About the Authors
Elena A. Usoshina
Eurogroup” LLC
Russian Federation
Russian Federation
Tatiana V. Suvorova
Rostov State Transport University
Russian Federation
Russian Federation
Arkady N. Solovyev
Don State Technical University
Russian Federation
Russian Federation
References
1. Gorshkov, А.G., Starovoytov, E.I., Tarlakovskiy, D.V. Teoriya uprugosti i plastichnosti. [Theory of elasticity and plasticity.] Moscow: Fizmatlit, 2002, 440 p. (in Russian).
2. Bio, М.А. Mekhanika deformirovaniya i rasprostraneniya akusticheskikh voln v poristoy srede. [Mechanics of deformation and propagation of acoustic waves in porous medium.] Mechanics. Periodic coll. of translations of foreign papers. 1963, vol. 6, no. 82, pp. 103–134 (in Russian).
3. Burridge, R., Keller, J.-B. Poroelasticity equations derived from microstructure. The Journal of the Acoustical Society of America, 1981, vol. 70, no. 4, pp. 1140–1146.
4. Scalia, A., Sumbatian, M.A. Contact problem for porous elastic half-plane. Journal of elasticity, 2000, vol. 60, no. 32, pp. 91–102.
5. Suvorova, Т.V., Usoshina, E.A. Kolebaniya sostavnogo geterogennogo sloya. [Oscillation of composite heterogeneous layer.] Ecological Bulletin of Research Centers of the Black Sea economic cooperation, 2010, no. 2, pp. 74–79 (in Russian).
6. Kolesnikov, V.I., Suvorova, T.V. Modelirovanie dinamicheskogo povedeniya sistemy «verkhnee stroenie zheleznodorozhnogo puti — sloistaya gruntovaya sreda». [Simulation of dynamic behavior of the system “track structure - layered soil ground”.] Moscow: VINITI RAN, 2003, 232 p. (in Russian).
7. Sveshnikov, А.G., Tikhonov, A.N. Teoriya funktsiy kompleksnoy peremennoy. [Complex variable theory.] Moscow: Nauka, 2004, 336 p. (in Russian).
8. Chao-Lung Yeh, Lo Wei-Cheng, Jan Chyan-Deng. An assessment of characteristics of acoustic wave propagation and attenuation trough eleven different saturated soils. American Geophysical Union. Fall Meeting. 2006, no. 12, p. 31.
9. Sumbatyan, M.A., Scalia, A., Usoshina, H.A. Dynamic Contact Problem for a Heterogeneous Layer with a Liquid Sheet on a Non-Deformable Foundation. Physics and Mechanics of New Materials and Their Applications (PHENMA 2015): Abstracts & Schedule оf 15 International Conference. Southern Federal University. Azov, 2015. Available at: http://phenma2015.math.sfedu.ru. pp. 239–240 (accessed: 16.07.16).
10. Hofmann, M., Most, T., Hofstetter, G. Parameter identification for partially saturated soil models. 2nd International Conference on Computational Methods in Tunneling. Ruhr University Bochum. Bochum: Aedificatio Publishers, 2009, pp. 1–4.
Review
For citations:
Usoshina E.A., Suvorova T.V., Solovyev A.N. Mathematical models of dynamic systems that include layered watered poroelastic foundations. Vestnik of Don State Technical University. 2016;16(3):10-16. (In Russ.) https://doi.org/10.12737/20215
Views:
607
Email this article 