{'fraction_non_alphanumeric': 0.02146690518783542, 'fraction_numerical': 0.0, 'mean_word_length': 5.357954545454546, '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}}
Reduced models in the medium-frequency range for general external structural-acoustic systems

This paper presents a theoretical approach for constructing a reduced model in the medium-frequency range in the area of structural acoustics for a general three-dimensional dissipative structure made of an anisotropic, inhomogeneous, viscoelastic bounded medium coupled with an external acoustic fluid. All the results presented can be used if the structure is made of beams, plates, and shells. The boundary value problem in the frequency domain and its variational formulation are presented. For a fixed medium-frequency band, an energy operator related to the structural-acoustic system is introduced. This operator is symmetric positive definite and has a countable set of positive eigenvalues. Its dominant eigensubspace allows a reduced model to be constructed using the Ritz–Galerkin method. A finite dimension approximation of the three-dimensional continuous case is presented and an effective construction of the dominant subspace using the subspace iteration method is developed. As an example, the reduced m...