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The transmission coefficient for vibrational waves crossing an abruptjunction between two thin elastic plates of different widths is calculated.These calculations are relevant to ballistic phonon thermal transport at lowtemperatures in mesoscopic systems and the Q for vibrations in mesoscopicoscillators. Complete results are calculated in a simple scalar model of theelastic waves, and results for long wavelength modes are calculated using thefull elasticity theory calculation. We suggest that thin plate elasticty theoryprovide a useful and tractable approximation to the full three dimensionalgeometry.Comment: 35 pages, including 12 figure

Elastic wave transmission at an abrupt junction in a thin plate with application to heat transport and vibrations in mesoscopic systems