{'fraction_non_alphanumeric': 0.010731052984574111, 'fraction_numerical': 0.0013413816230717639, 'mean_word_length': 5.040485829959514, '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}}
Finite element-optimization methods for the active control of radiated sound from a plate structure

Optimization of the geometry and the excitation voltage applied to a piezoelectric actuator embedded on a plate structure is studied to reduce the radiation of sound into the space above the plate when the plate is excited by the acoustic pressure field produced by a noise source located below the plate. In the more realistic case, one could consider the plate to comprise of one wall of an enclosure containing a noise source. Finite element modeling is used for the plate structure that includes a full description of coupled fields in the piezoelectric actuator and elastic plate. Since the use of three-dimensional (3D) elements in the plate structure tends to stiffen the structure unnecessarily, a combination of shell elements for the plate and 3D elements for the actuator with transition elements to connect the two regions have also been implemented. Clamped boundary conditions are assumed in the calculations. The cost function of optimization is the sound energy radiated onto a hemispherical surface of given radius and the optimization parameters are size of the piezoelectric actuator as well as the amplitude and phase of the voltage applied to the actuator. Good results are obtained for both resonance and off-resonance conditions. The optimization is robust enough that even if the pattern of the acoustic pressure field changes, the radiated sound is still minimized.