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Stability of a viscoelastic pipe filled with a moving fluid. (English) Zbl 0882.35120

Summary: Sufficient stability conditions are derived for transversal oscillations of a thin-walled viscoelastic pipe filled with a moving fluid. By using two different approaches, explicit expressions are developed for the critical flow velocities. In particular, steady flow and time-periodic flow are considered. The effect of material and geometrical parameters on the critical velocity is studied numerically.

MSC:

35Q72 Other PDE from mechanics (MSC2000)
35R35 Free boundary problems for PDEs
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74H55 Stability of dynamical problems in solid mechanics
45K05 Integro-partial differential equations
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