{'fraction_non_alphanumeric': 0.01764705882352941, 'fraction_numerical': 0.00392156862745098, 'mean_word_length': 5.503184713375796, '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}}
Study of the frequency spectrum of forced vibrations of piezoceramic bars polarized in length direction

The approximate one-dimensional equations of motions and charge equations of electrostatics, governing coupled length-extensional, width-stretch and symmetric width-shear vibrations of rectangular finite piezoelectric ceramic bar of hexagonal symmetry 6mm, polarized in the length direction, are presented. The bars with electrodes on the faces perpendicular to the length are supposed. These equations are used to study the frequency spectrum of coupled vibrations of PZT bar with variable cross section excited by the electric field parallel with the length. The influence of the width to thickness ratio on the resonance frequency spectrum is discussed. Increasing the ratio of width to thickness, the coupling of higher vibration modes in the frequency spectrum is more significant. The computed frequency spectra are compared with the experimental data, obtained for PZT ceramics samples of APC841 (hard) type.