Showing papers by "Yuriko Renardy published in 1987"
TL;DR: In this paper, it is shown that the Timoshenko beam can be uniformly stabilized by means of a boundary control, and a numerical study on the spectrum is also presented, showing that the beam is uniformly stabilized with respect to the boundary control.
Abstract: It is shown that the Timoshenko beam can be uniformly stabilized by means of a boundary control. A numerical study on the spectrum is also presented.
379 citations
TL;DR: In this article, the linear stability of Couette flow composed of two layers of immiscible fluids, one lying on top of the other, is considered for the special case when the two fluids have similar mechanical properties.
Abstract: The linear stability of Couette flow composed of two layers of immiscible fluids, one lying on top of the other, is considered for the special case when the two fluids have similar mechanical properties. The interfacial eigenvalue is found in closed form by considering the two‐fluid problem as a perturbation of the one‐fluid problem. The importance of the role played by the viscosity difference, when one of the fluids is in a thin layer, is illustrated.
71 citations
TL;DR: In this paper, the linear stability of plane three-layer vertical Poiseuille flow is considered and the ability of heuristic reasoning to predict which arrangements are more likely to be observed is tested.
Abstract: The linear stability of plane three‐layer vertical Poiseuille flow is considered. The layers are composed of two immiscible fluids, one next to the walls and one centrally located. The fluids have different viscosities and densities and surface tension effects are included. Intuitively, an analogy with the concentric Hagen–Poiseuille flow is expected and the similarities and differences are investigated. The ability of heuristic reasoning to predict which arrangements are more likely to be observed is tested. Numerical results concerning low Reynolds numbers, as well as the behavior of eigenvalues close to the first criticality of the one‐fluid problem, are presented.
48 citations
01 Dec 1987
TL;DR: In this paper, boundary feedback schemes for stabilizing flexural vibrations in a linear viscoelastic beam are studied, and it is shown that in the Euler-Bernoulli model an arbitrarily small feedback delay can cause unbounded vibrations with arbitrarily large exponential growth rates.
Abstract: Boundary feedback schemes for stabilizing flexural vibrations in a linear viscoelastic beam are studied. It is shown that in the Euler-Bernoulli model an arbitrarily small feedback delay can cause unbounded vibrations with arbitrarily large exponential growth rates. For the Timoshenko beam, in the purely elastic case, a contrasting result is given, and formulas for decay rates of high frequency modes are developed for the case of no feedback delay. Numerical results for various no-delay cases are summarized.
11 citations