Effect of local enlargement on the trapped modes of infinite or semi-infinite membrane strips

• Vibrating membranes composed of long strips with local enlargement may lead to trapped modes.
• Often there exists a much lowered fundamental frequency which dominates the vibration mode.
• Results are applicable to vibrating plates, acoustic and EM waveguides, and quantum waveguides.

The vibration of infinite or semi-infinite membrane strip with a local enlargement is studied. An efficient domain decomposition and matching method is used to accurately solve the governing Helmholtz equation. Due to the enlargement, the fundamental frequency is decreased considerably and the corresponding vibration mode is effectively localized near the junction. The results are particularly significant to quantum waveguides.