Abstract
Two averaged (effective) models corresponding to transverse and longitudinal oscillations in a periodic combined stratified medium are constructed. The medium considered consists of alternating layers of an isotropic viscoelastic material and a viscous compressible fluid. The dependence of the qualitative characteristics of the spectra of the averaged models on the linear dimensions of the stratified medium specimen is investigated.
Similar content being viewed by others
References
E. Sanchez-Palencia, Non-HomogeneousMedia and Vibration Theory (Springer, Berlin, 1980).
G. Nguetseng, “A General Convergence Result for a Functional Related to the Theory of Homogenization,” SIAM J. Math. Anal. 20(3), 608–623 (1989).
R.P. Gilbert and A. Mikelić, “Homogenizing the Acoustic Properties of the Seabed: Pt I,” Nonlinear Anal. 40(1), 185–212 (2000).
A.M. Meirmanov, “Nguetseng’s Two-Scale Convergence Method in Problems of Fluid Flow and Seismic Acoustics in Elastic Porous Media,” Sib. Mat. Zh. 48(3), 645–667 (2007).
A. Meirmanov, “A Description of Seismic Acoustic Wave Propagation in Porous Media via Homogenization,” SIAM J. Math. Anal. 40(3), 1272–1289 (2008).
A.S. Shamaev and V.V. Shumilova, “Averaging the Acoustic Equations for a Partly Perforated Viscoelastic Material with a Viscous Fluid,” Dokl. Ros. Akad. Nauk 436(2), 199–202 (2011).
A.S. Shamaev and V.V. Shumilova, “Averaging the Acoustics Equations for a Viscoelastic Material with Channels Filled with a Viscous Compressible Fluid,” Fluid Dynamics 46(2), 250–261 (2011).
D.A. Kosmodemyanskii and A.S. Shamaev, “Spectral Characteristics of Certain Problems inMechanics of Strongly Inhomogeneous Media,” Izv. Ros. Akad. Nauk, Mekh. Tverd. Tela, No. 6, 75–114 (2009).
A.V. Gavrikov and A.S. Shamaev, “Certain Problems of Emulsion Acoustics,” Dokl. Ros. Akad. Nauk 434(1), 42–46 (2010).
V.V. Vlasov, A.A. Gavrikov, S.A. Ivanov, et al., “Spectral Characteristics of Combined Media,” in Contemporary Mathematics and Its Applications [in Russian] 64, 105–119 (2009).
L.D. Akulenko and S.V. Nesterov, “Inertial and Dissipative Characteristics of a Porous Medium Filled with a Viscous Fluid,” Izv. Ros. Akad. Nauk, Mekh. Tverd. Tela, No. 1, 109–119 (2005).
A.S. Shamaev and V.V. Shumilova, “On the Spectrum of an Integro-Differential Equation That Arises in the Theory of Viscoelasticity,” in Problems of Mathematical Analysis [in Russian] 63, 189–192 (2012).
Additional information
Original Russian Text © A.S. Shamaev, V.V. Shumilova, 2013, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2013, Vol. 48, No. 1, pp. 17–25.
Rights and permissions
About this article
Cite this article
Shamaev, A.S., Shumilova, V.V. Spectrum of one-dimensional oscillations in the combined stratified medium consisting of a viscoelasticmaterial and a viscous compressible fluid. Fluid Dyn 48, 14–22 (2013). https://doi.org/10.1134/S0015462813010031
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462813010031