This article aims at analytically solving the free vibration problem of rectangular thin plates with one corner free and its opposite two adjacent edges rotationally-restrained, which is difficult to handle by conventional semi-inverse approaches such as the Levy solution and Naiver solution, etc. Based on the classical Fourier series theory, this work presents a first endeavor to treat the two-dimensional half-sinusoidal Fourier series, which is quite similar to the Navier’s form solution, as the solution form of plate deflection. By utilizing the orthogonality of the present trial function and the Stoke’s transformation technique, the present solution procedure converts the complicated plate problem into solving sets of linear algebra equations, which heavily decreases the difficulties. Therefore, the present approach enables one to solve the title problem in a unified, simple and straightforward way, which is very easily implemented by researchers. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through utilizing different types of Fourier series and it can be extended for further dynamic/static analysis of plates under different shear deformation theories. Moreover, without any extra derivation processes, new, precise analytical free vibration solutions for plates under three non-Levy-type boundary conditions are also obtained by choosing different rotating fixed coefficients. Consequently, we present more than 400 comprehensive free vibration results for plates with classical/non-classical boundaries, all the present results are confirmed by FEM/analytical solutions and can be used as benchmark data for further research.

In order to solve the problem of intelligent detection of damage of modern concrete structures under complex constraints, an improved self-organizing mapping (SOM) neural network model algorithm was proposed to construct an accurate identification model of concrete structure damage. Based on the structure and algorithm of the SOM network model, the whole process of the core construction of the concrete structure damage identification network model is summarized. Combined with the damage texture characteristics of concrete structures, through the self-developed 3D laser scanning system, an improved method based on a small number of samples to effectively improve the effectiveness of network input samples is proposed. Based on the principle of network topology map analysis and its image characteristics, a SOM model improvement method that can effectively improve the accuracy of the network identification model is studied. In addition, based on the reactive powder concrete bending fatigue loading test, the feasibility and accuracy of the improved method are verified. The results show that the improved SOM concrete structure damage identification model can effectively identify unknown neuron categories in a limited sample space, and the identification accuracy of the SOM network model is improved by 4.69%. The proposed improved SOM model method fully combines the network topology and its unique image features and can accurately identify structural damage. This research contributes to the realization of high-precision intelligent health monitoring of damage to modern concrete structures. In addition, it is of great significance for the timely detection, identification and localization of early damage to structures.

An improved concrete structure health monitoring method based on G-S-G is proposed, which fully combines an optimized Gray-Level Co-occurrence Matrix (GLCM) with an improved Self-Organizing Map (SOM) neural network to achieve accurate and real-time concrete structure health monitoring. First of all, in order to obtain a dynamic image of the crack damage region of interest (ROI) with clear contrast and obvious target, the image acquisition system and image optimization method are used to process the damaged image. Moreover, in order to realize the accurate location of crack damage, crack damage identification research based on GLCM-SOM effectively eliminates the interference of honeycomb and pothole damage on crack damage. In order to obtain the indicators for monitoring the health status of the structure, the damage characteristics and probability distribution characteristics of the concrete structure in the gray level co-occurrence matrix are combined to extract the probability range index (PRI). On the basis of extracting the crack damage index, in order to verify the reliability of the sensitive feature index, starting from the two dimensions of damage texture feature and data expansion, through reverse research of the damage model, the damage index of accurately locating the crack damage was selected. It follows that the final sensitive indicators: entropy (ENT) and PRI can be used for structural health monitoring because of their strong damage characterization ability and sensitivity to damage characteristics. This research shows that is helpful to realize the high precision intelligent concrete structure health monitoring of modern concrete structure crack damage.

This study presents an innovative approach to hourly demand forecasting for bike-sharing systems using a multi-attribute, edge-weighted, Gated Graph Convolutional Network (GGCN). It addresses the challenge of imbalanced bike borrowing and returning demands across stations, aiming to enhance station utilization rates. The proposed model employs GGCNs to capture spatial relationships between stations and incorporates both current and historical data via a gating mechanism to account for temporal dependencies. By integrating three key edge-weight attributes—stations distance, travel duration, and correlation—into a multi-attribute graph framework, the model significantly improves predictive accuracy for user travel patterns. Additionally, user characteristics are included as node features, enabling a more comprehensive analysis. The study utilizes the 2020 dataset from Jersey City’s bike-sharing system, starting with the application of the Isolation Forest algorithm to detect and filter anomalous data points. A detailed analysis of the temporal, spatial, and user-related factors is conducted to examine how these features interact and shape demand patterns in the bike-sharing network. The dataset is segmented by season to account for seasonal variations. The results demonstrate that the multi-attribute, edge-weighted GGCN outperforms baseline and single-attribute models, achieving a Mean Absolute Error (MAE) of 0.521 and Mean Squared Error (MSE) of 0.918 for spring and autumn, and an MAE of 0.307 and MSE of 0.608 for summer and winter.