{'fraction_non_alphanumeric': 0.011959521619135235, 'fraction_numerical': 0.0, 'mean_word_length': 5.325581395348837, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On the Effect of Edge Boundaries on Nearly Trapped Vibrations of Contoured Rectangular Quartz Resonators

Energy trapped modes in contoured quartz plates can accurately be predicted introducing a slow variation of the thickness into the asymptotic dispersion equation of quasi-thickness vibrations. Solving the associated partial differential equation, only solutions which do not diverge at infinity are usually retained. This restriction is not made in this paper. Thus, the solutions are parabolic cylinder functions determined by a parameter related to boundary conditions at the edges of the plate. Hermite functions as well as trigonometric solutions are limiting cases of those function;, the use of which is possible either in an analytical model recently obtained or in a model taking into account the mixed partial derivatives terms by an approximate perturbation method. In both cases, the dependence of the frequency versus the lateral dimensions of the plate can be computed, thereby facilitating the selection of proper values of the radius of curvature for a desired mode.