Abstract
The Helmholtz equation with zero boundary conditions is important in the vibration of membranes, simply-supported plates, and electromagnetic and quantum waveguides. Trapped modes, with a lowered frequency and limited local effect, may exist for infinite strips with local bends or enlargements. Infinite strips with a cross bulge, with an S bend and with a U bend are studied using an efficient eigenfunction expansion and domain decomposition method. As the bulge become larger, more trapped modes with more complexity appear. Some geometries do not support trapped modes at all. These results are new.
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