**
The Dynamics of an Elastic Membrane Using the Impulse Method
**

(R. Cortez and D. A. Varela)
#### Abstract

A nonlinear analysis of the motion of a closed elastic membrane under
tension separating two incompressible, inviscid fluids in two
dimensions is presented. The analysis is based on a small-amplitude
perturbation of an exact solution. The equations of motion for the
Fourier coefficients of the solution are developed to two orders
beyond the leading-order problem. The nonlinear terms in the
equations depict the coupling of the Fourier modes and account for the
temporal variation of the tension. The last order of the expansion is
used to compute frequency corrections to the driving modes. Solutions
for various problems are found and compared with a numerical method
based on impulse variables. The results show that the numerical
periods of the oscillations approach the periods predicted by the
perturbation analysis as the numerical smoothing parameter is reduced.
This gives validation to the use of impulse methods for free-boundary
motion with surface forces.

* J. Comput. Phys., ***138** (1997), pp. 224-247

**LaTeX Bibliography:**
@article{CortezVarela1997,
author = {Ricardo Cortez and Douglas A. Varela},
title = {The dynamics of an elastic membrane using the impulse method},
journal = {J. Comput. Phys.},
volume = {138},
number = {1},
month = {Nov.},
year = {1997},
pages = {224--247}
}

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