The rubber membrane and the solution of Laplace's equation

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, , Citation W Fulop 1955 Br. J. Appl. Phys. 6 21 DOI 10.1088/0508-3443/6/1/309

0508-3443/6/1/21

Abstract

Previous theory of the rubber membrane predicted Laplace's equation to hold only for small inclinations of the membrane to its horizontal undisplaced position. In practice the equation has, however, been found to hold for quite large inclinations. In addition, it has been observed that the motion of any point in the membrane is purely vertical for vertical displacements of the "electrodes." This suggested that it is the horizontal component of the tension which remains constant and equal to the tension in the undisplaced position. On this assumption it is found that Laplace's equation holds without restriction. It is interesting to note that this assumption is equivalent to assuming that vertical displacements satisfy Hooke's law, which experiments have shown to hold for quite large inclinations.

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10.1088/0508-3443/6/1/309