Propagation of weakly nonlinear waves in fluid-filled thick viscoelastic tubes


Demiray H.

APPLIED MATHEMATICAL MODELLING, cilt.23, sa.10, ss.779-798, 1999 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 10
  • Basım Tarihi: 1999
  • Doi Numarası: 10.1016/s0307-904x(99)00012-8
  • Dergi Adı: APPLIED MATHEMATICAL MODELLING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.779-798
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

In the present work, we studied the propagation of small-but-finite-amplitude waves in a prestressed thick walled viscoelastic tube filled with an incompressible inviscid fluid. In order to include the dispersion, the wall's inertial and shear effects are taken into account in determining the inner pressure-inner cross-sectional area relation. Using the reductive perturbation method, the propagation of weakly nonlinear waves in the long-wave approximation is investigated. After obtaining the general evolution equation in the long-wave approximation, by a proper scaling, it is shown that this general equation reduces to the well-known evolution equations such as the Burgers, Korteweg-de Vries (KdV), Koteweg-de Vries-Burgers (KdVB) and the generalized Burgers' equations. By proper re-scaling of the perturbation parameter, the modified form of the evolution equations is also obtained. The variations of the travelling wave profile with initial deformation and the viscosity coefficients are numerically evaluated and the results are illustrated in some figures. (C) 1999 Elsevier Science Inc. All rights reserved.