This study introduces an innovative model-order reduction (MOR) technique that integrates boundary element and finite element methodologies, streamlining the analysis of wideband vibro-acoustic interactions within aquatic and aerial environments. The external acoustic phenomena are efficiently simulated via the boundary element method (BEM), while the finite element method (FEM) adeptly captures the dynamics of vibrating thin-walled structures. Furthermore, the integration of isogeometric analysis within the finite element/boundary element framework ensures geometric integrity and maintains high-order continuity for Kirchhoff–Love shell models, all without the intermediary step of meshing. Foundational to our reduced-order model is the application of the second-order Arnoldi method coupled with Taylor expansions, effectively eliminating the frequency dependence of system matrices. The proposed technique significantly enhances the computational efficiency of wideband vibro-acoustic coupling analyses, as demonstrated through numerical simulations.

In recent years, the rapid advancement of materials science has underscored the significance and complexity of understanding and optimizing the properties of piezoelectric materials. Traditional analytical methods have encountered difficulties in addressing the challenges posed by variable material compositions and intricate processing conditions. However, deep neural networks (DNNs) present new opportunities in this field due to their robust capabilities in nonlinear data processing and pattern recognition. This study employs DNN to model the relationship between the composition and processing conditions of piezoelectric materials and their electrical properties. Through quenching experiments, it was observed that the electrical properties of Na _0.5 Bi _0.5 TiO ₃ -based ceramics are positively correlated with local polar heterogeneity. This phenomenon was further validated by manipulating the local polar heterogeneity through Bi or Sr nonstoichiometric modifications. Subsequently, a DNN model characterized by local polarity heterogeneity was developed. After training on extensive high-quality experimental data, the DNN model demonstrated exceptional prediction accuracy and effectively elucidated the underlying complex mechanisms governing material properties. The findings indicate that DNN can accelerate the development and optimization of new piezoelectric materials, provide guidance for experimental design, and significantly enhance research and development efficiency. The successful application of this research strongly supports the expansion of deep learning technology in materials science.

Ferroelectric materials have emerged as significant research hotspots within the field of materials science and engineering, primarily due to their unique electrical properties. However, the electrical characteristics of these materials are influenced by various factors, including material composition, microstructure, and preparation processes, which introduce considerable randomness and uncertainty. Traditional experimental and simulation methods are often insufficient for capturing these complex interactions, thereby hindering the prediction and optimization of material performance. This paper presents a novel approach for predicting the electrical properties of ferroelectric materials by utilizing deep neural networks (DNNs). The DNNs are trained using experimental data and serve as a proxy model to predict critical electrical properties, such as the dielectric constant and dielectric peak. The (1- x)Na_0.5Bi_0.5TiO₃- xSrZrO₃ ceramics were synthesized via the solid-state reaction method, and both the phase structure and electrical properties of NBT- xSZ were measured. The experimental results indicate that the DNN model effectively captures the intricate influences of factors such as material composition, preparation processes, and microstructure on electrical properties. The discrepancy between predicted values and experimental results remains within an acceptable range. By comparing the absolute error (<5) between measured and predicted data, alongside evaluation metrics such as MAPE, SMAPE, and R², the practicality and reliability of the DNN model are substantiated. The strong performance of this model not only accelerates the development of new materials but also enhances the optimization of the performance of existing materials.