{'fraction_non_alphanumeric': 0.01337613697164259, 'fraction_numerical': 0.0, 'mean_word_length': 5.131147540983607, '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}}
Remote Excitation of Trapped Energy Modes in Plates and Pipes and its Applications to Sensors and Non-Destructive Testing

Trapped energy modes of thickness twist and thickness shear vibrations in a plate have been widely used in quartz crystal devices for frequency generation and selection. Similar trapped energy modes can exist in torsional waves in a solid cylinder, axially symmetric torsional waves in a plate, torsional waves in a hollow cylinder and circumferential thickness twist waves in a hollow cylinder. Piezoelectric or magnetostrictive transduction has been used for direct excitation of these modes. This paper presents a means of remote excitation of these modes through mode conversion from a propagating mode. The lowest mode of thickness twist waves in a plate, torsional waves in a plate or a cylinder is non-dispersive and hence can propagate a long distance without distortion of waveform. When it hits a boundary of trapped energy region, a part of energy is converted into the trapped energy mode. This reflects in a change of mechanical impedance or reflection coefficient, which allows a measurement of resonant frequency and Q of the trapped mode. Characteristics of trapped modes are sensitive to mass and viscous loading, change of thickness and corrosion. Hence it can be utilized in applications to sensors like QCM (quartz crystal microbalance) and non-destructive testing of plates, shells and pipes. Plural regions of trapped mode with different resonant frequencies can be located in a single plate or cylinder, so that simultaneous remote measurement of all sensors is possible. An analysis of degree of mode conversion at a boundary and its reaction on mechanical impedance is presented based on multiple transmission line model. Experimental observations of responses to both impulse and burst waveforms agree with the analysis.