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The ponding on an inflated membrane tube is studied. Membrane tubes have the advantage of zero leakage and ease of transportation and set-up. A novel related problem is the membrane trough which can be used to contain water and does not need anchoring. These problems depend on two non-dimensional parameters which characterize membrane tension and pressure. Perturbation solutions to second order are...
The Helmholtz equation governs the dynamics of membranes and waveguides. Using the mode matching method, trapped modes are found for an infinite strip with a segment of inhomogeneity. The exact frequencies and mode shapes are determined as a function of density ratio and length of the segment. Nonuniqueness and nonexistence are demonstrated.
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