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The dynamics of an elastic membrane using the impulse method. (English) Zbl 0910.73035
The authors study the interface between two incompressible fluids moving inside and outside of a closed, flexible, elastic membrane. The forces along the membrane are given by the product of the curvature and a time-dependent tension which is a function of the length of the membrane. A nonlinear analysis of the problem is based on a small-amplitude perturbations using a circular membrane as the base solution. Solution for various cases are found and compared with numerical solutions obtained by a numerical method based on impulse variables. Various versions of the problem can be used as models for various physical phenomena, in particular for the modeling of the blood flow in heart chamber.

MSC:
74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
74S30 Other numerical methods in solid mechanics (MSC2010)
74L15 Biomechanical solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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