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Keywords = analytic element method

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22 pages, 6693 KB  
Article
Layered Multi-Objective Optimization of Permanent Magnet Synchronous Linear Motor Considering Thrust Ripple Suppression
by Shiqi Xu, Jinhua Du and Jing Zhang
Appl. Sci. 2026, 16(2), 969; https://doi.org/10.3390/app16020969 (registering DOI) - 17 Jan 2026
Abstract
In this study, a layered multi-objective optimization design method is proposed for a segmented skewed pole permanent magnet synchronous linear motor (PMSLM), considering thrust ripple suppression. Based on a 2-D analytical model, the effects of end force, cogging force, and winding asymmetry force [...] Read more.
In this study, a layered multi-objective optimization design method is proposed for a segmented skewed pole permanent magnet synchronous linear motor (PMSLM), considering thrust ripple suppression. Based on a 2-D analytical model, the effects of end force, cogging force, and winding asymmetry force on thrust ripple in PMSLM are analyzed, and the correctness is verified using finite element analysis and experiments. On this basis, a layered multi-objective optimization method is proposed. The whole optimization is divided into three layers. Metamodels of optimal prognosis are established to optimize the structural parameters in a layered manner, achieving a compromise between reducing thrust ripple and increasing average thrust. The effectiveness of the layered multi-objective optimization method is verified through simulation and prototype experiments. The layered structure aims to improve efficiency while ensuring computational accuracy. Full article
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34 pages, 3432 KB  
Article
A Study of the Technological Features of Bronze Anthropomorphic Sculpture Production from the Jin Dynasty (1115–1234 AD) from the Collection of the IHAE FEB RAS
by Igor Yu Buravlev, Aleksandra V. Balagurova, Denis A. Shahurin, Nikita P. Ivanov and Yuri G. Nikitin
Heritage 2026, 9(1), 33; https://doi.org/10.3390/heritage9010033 - 16 Jan 2026
Viewed by 27
Abstract
This paper presents the results of a comprehensive technological study of three bronze sculptures from the Jin Empire period (1115–1234 AD) from the collection of the Museum of Archaeology and Ethnography at the Institute of History, Archaeology and Ethnography of the Peoples of [...] Read more.
This paper presents the results of a comprehensive technological study of three bronze sculptures from the Jin Empire period (1115–1234 AD) from the collection of the Museum of Archaeology and Ethnography at the Institute of History, Archaeology and Ethnography of the Peoples of the Far East, Far Eastern Branch of the Russian Academy of Sciences (IHAE FEB RAS). Using photon-counting computed tomography (PCCT) and energy-dispersive X-ray spectroscopy (EDS), the production techniques were reconstructed, differences in alloy composition were identified, and specific features of the casting processes were determined. Tomographic analysis revealed two fundamentally different manufacturing approaches: a multi-stage technology involving the use of different alloys and the assembly of separately cast elements, and a single-cast technology with a homogeneous structure. Elemental analysis of the three sculptures using EDS demonstrated significant compositional variability—from 21% to 67% copper and from 9% to 69% tin in different parts of the objects—confirming the complexity of the technological processes. An expanded study of 20 bronze sculptures using portable X-ray fluorescence analysis (pXRF) allowed for the identification of four typological alloy groups: classic balanced lead–tin bronzes (Cu 30–58%, Sn 16–23%, Pb 16–28%), high-lead bronzes (Pb up to 52%), high-tin bronzes (Sn up to 30%), and low-tin alloys (Sn less than 11%). The morphological features of the sculptures suggest one of their possible interpretations as ancestor spirits used in ritual practices. The research findings contribute to the study of Jurchen metallurgical traditions and demonstrate the potential of interdisciplinary, non-destructive analytical methods for reconstructing the technological, social, and cultural aspects of medieval Far Eastern societies. Full article
(This article belongs to the Topic 3D Documentation of Natural and Cultural Heritage)
16 pages, 3266 KB  
Article
Selenium Quantification in Soil by LIBS
by Alexandra V. Rogachevskaya, Vasily N. Lednev, Pavel A. Sdvizhenskii, Igor Y. Savin, Sergey V. Gudkov, Alexey S. Dorohov and Andrey Y. Izmaylov
Physics 2026, 8(1), 9; https://doi.org/10.3390/physics8010009 - 16 Jan 2026
Viewed by 37
Abstract
Laser-induced breakdown spectrometry (LIBS), known as an express analysis technique, is for the first time applied in this study for determining selenium in soil. Modern agriculture requires elemental analysis methods to perform the continuous automated online control of microelement content in soil. However, [...] Read more.
Laser-induced breakdown spectrometry (LIBS), known as an express analysis technique, is for the first time applied in this study for determining selenium in soil. Modern agriculture requires elemental analysis methods to perform the continuous automated online control of microelement content in soil. However, selenium has never been quantitatively determined in soil by LIBS so far. Different sample preparation techniques (loose soil powder, mounted on adhesive tape and tableted soil) are employed here for LIBS determination of selenium in soil. The optimal choice of analytical line is challenging for selenium because of spectral interference with the minor and major soil components (Fe, Si, Zn, Al, Sb), but the Se I 196.09 nm line has the lowest spectral interference. A limit of detection of 3 mg/kg for selenium in soil is achieved in the present study using LIBS. The analytical performance of tape-mounted and loose soil powder samples with appropriate data averaging is found to be comparable to that achieved for tablets. Full article
(This article belongs to the Section Applied Physics)
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32 pages, 1466 KB  
Review
Machine Learning Applications in the Mechanical Analysis of Nanomaterials and Nanostructures
by Mostafa Sadeghian, Arvydas Palevicius, Paulius Griskevicius and Giedrius Janusas
Appl. Sci. 2026, 16(2), 918; https://doi.org/10.3390/app16020918 - 15 Jan 2026
Viewed by 109
Abstract
Machine learning (ML) is increasingly used to address the computational complexity and multiscale nature of mechanical analysis in nanomaterials and nanostructures. Traditional analytical, numerical, and atomistic approaches, such as continuum mechanics, finite element methods, and molecular dynamics (MD), often suffer from high computational [...] Read more.
Machine learning (ML) is increasingly used to address the computational complexity and multiscale nature of mechanical analysis in nanomaterials and nanostructures. Traditional analytical, numerical, and atomistic approaches, such as continuum mechanics, finite element methods, and molecular dynamics (MD), often suffer from high computational cost or limited scalability when applied to nanoscale systems. Recently, ML techniques have been increasingly used to predict mechanical properties, analyze static and dynamic responses, and solve governing equations of nanostructures to improve efficiency and accuracy. This review provides a comprehensive overview of ML applications in the mechanical analysis of nanomaterials and nanostructures, including mechanical property prediction, static response analysis, and vibration analysis. Various ML techniques based on the property or type of the mechanical problem are discussed in detail. The review highlights current trends and provides structured guidance for future research on reliable and physically consistent ML methods for nanoscale mechanical analysis. Full article
20 pages, 2326 KB  
Article
Stability of Composite Plates with a Dense System of Ribs in Two Directions
by Jakub Marczak, Martyna Rabenda and Bohdan Michalak
Materials 2026, 19(2), 322; https://doi.org/10.3390/ma19020322 - 13 Jan 2026
Viewed by 90
Abstract
This paper presents an easy-to-use analytical method for stability analysis of composite plates with dense bidirectional microstructure. The main characteristic feature of such a defined composite is that due to its periodic nature the obtainable governing partial differential equations are characterised by discontinuous, [...] Read more.
This paper presents an easy-to-use analytical method for stability analysis of composite plates with dense bidirectional microstructure. The main characteristic feature of such a defined composite is that due to its periodic nature the obtainable governing partial differential equations are characterised by discontinuous, strongly oscillating coefficients. Such cases bring many difficulties during derivation of their solution. In order to simplify calculations, the initial governing equations are transformed with the use of the tolerance averaging technique, so a system of partial differential equations with constant coefficients is obtained. The most important finding of the presented work is that the form of the mentioned equations is similar to the classic equations, which describe the stability issue of the thin homogeneous plate. Consequently, the analytical solution to such issues is easily obtainable. Moreover, when compared to, for example, finite element method (FEM) analysis, it requires substantially less computation resources, which can be perceived as its superior feature. Therefore, the proposed method is convenient for engineering applications. In this paper, a comparative analysis of the results obtained from the proposed analytical models with the results obtained from the FEM has been carried out. The impact of materials and dimensions of microstructure on the values of critical normal and shear forces has also been analysed. Full article
(This article belongs to the Section Mechanics of Materials)
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19 pages, 4811 KB  
Article
Research on Structure and Electromagnetic Properties of a Dual-Channel Coupled Radial Magnetic Field Resolver
by Hao Wang, Jundi Wang, Hong Chen and Changchao Li
Vehicles 2026, 8(1), 18; https://doi.org/10.3390/vehicles8010018 - 13 Jan 2026
Viewed by 87
Abstract
This paper presents a kind of dual-channel coupled radial magnetic field resolver (DCCRMFR). The exciting winding and signal winding of this resolver adopt the structure of orthogonal phase. The number of turns and distribution of the four phase signal winding have been designed. [...] Read more.
This paper presents a kind of dual-channel coupled radial magnetic field resolver (DCCRMFR). The exciting winding and signal winding of this resolver adopt the structure of orthogonal phase. The number of turns and distribution of the four phase signal winding have been designed. The rotor has a double-wave magnetic conductive material structure. The variable reluctance mechanism between the stator and the rotor is derived by analytical method, and the feasibility of changing the coupling area for variable reluctance is obtained. The inductance of DCCRMFR was theoretically derived through the winding function method and combined with the finite element simulation method to obtain the inductance variation law and verify the correctness of the resolver design. Then simulation analysis was conducted on the output signal of DCCRMFR to extract the total harmonic distortion (THD) of the envelope of the electromotive force (EMF) output from the signal winding. Taking THD as the optimization objective, the optimized DCCRMFR simulation model is obtained by analyzing the air-gap length between the stator and the rotor and the thickness ratio of rotor. Finally, experimental measurements were conducted on a prototype model of a two pole pairs DCCRMFR, and the measurement results were compared and analyzed with simulation results to verify the correctness of the structural design and optimization of this DCCRMFR. Full article
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35 pages, 8323 KB  
Article
Evaluating Digital Marketing, Innovation, and Entrepreneurial Impact in AI-Built vs. Professionally Developed DeFi Websites
by Nikolaos T. Giannakopoulos, Damianos P. Sakas and Nikos Kanellos
Future Internet 2026, 18(1), 48; https://doi.org/10.3390/fi18010048 - 13 Jan 2026
Viewed by 195
Abstract
This study evaluates whether an AI-built DeFi website case can match professionally developed DeFi platforms in digital marketing performance, innovation-related strategic behavior, and entrepreneurial impact. Using a multi-method design, we compare five established DeFi websites (Aave, Lido, Curve, MakerDAO, Uniswap) against one AI-built [...] Read more.
This study evaluates whether an AI-built DeFi website case can match professionally developed DeFi platforms in digital marketing performance, innovation-related strategic behavior, and entrepreneurial impact. Using a multi-method design, we compare five established DeFi websites (Aave, Lido, Curve, MakerDAO, Uniswap) against one AI-built interface (Nexus Protocol). The analysis is designed as a five-platform benchmarking study of established professional DeFi websites, complemented by one AI-built case (Nexus Protocol) used as an illustrative comparison rather than a representative class of AI-built interface. The objectives are to (i) test differences in traffic composition and acquisition strategies, (ii) quantify how engagement signals predict authority and branded traffic, (iii) examine cognitive processing and trust-cue attention via eye tracking, and (iv) model emergent engagement and authority dynamics using agent-based simulation (ABM). Web analytics (March–October 2025) show significant variation in traffic composition across professional platforms (ANOVA F = 3.41, p = 0.0205), while regression models indicate that time on site and pages per visit positively predict Authority Score (R2 = 0.61) and Branded Traffic (R2 = 0.55), with bounce rate exerting an adverse effect. PCA and k-means clustering identify three strategic archetypes (innovation-driven, balanced-growth, efficiency-focused). Eye-tracking results show that professional interfaces generate tighter fixation clusters and shorter scan paths, indicating higher cognitive efficiency. In contrast, fixation on key UI elements and trust cues is comparable across interface types. ABM outputs further suggest that reduced engagement depth in the AI-built interface yields weaker long-run branded-traffic and authority trajectories. Overall, the study provides an integrated evaluation framework and evidence-based implications for AI-driven interface design in high-trust fintech environments. Full article
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21 pages, 2290 KB  
Article
A Helical Gear Meshing Stiffness Model Incorporating Friction Effects and Contact Deformation
by Zhiwen Yang, Kangfan Yu and Jianrun Zhang
Appl. Sci. 2026, 16(2), 804; https://doi.org/10.3390/app16020804 - 13 Jan 2026
Viewed by 112
Abstract
The accurate calculation of gear time-varying mesh stiffness is of significant importance for the dynamic modeling of gear systems. Currently, research on calculation methods for helical gear mesh stiffness is relatively limited, with the primary approaches being finite element methods and analytical methods. [...] Read more.
The accurate calculation of gear time-varying mesh stiffness is of significant importance for the dynamic modeling of gear systems. Currently, research on calculation methods for helical gear mesh stiffness is relatively limited, with the primary approaches being finite element methods and analytical methods. This paper proposes an optimized helical gear meshing stiffness model. Building upon the slice potential method, this approach comprehensively accounts for the effects of tooth-surface friction and local contact deformation. Results indicate that tooth surface friction causes abrupt changes in meshing stiffness values, while local contact deformation leads to an overall decrease in meshing stiffness values. To validate the application value of the optimized calculation method, the contact line method was replaced with the optimized slice potential energy method for simulating the external sound field of locomotive traction transmission systems. Comparisons with actual measurement data revealed that the sound pressure level data from this study’s meshing stiffness model align more closely with experimental results than those from the contact line method model, with the maximum error decreasing from 5% to 2.2%, effectively enhancing the accuracy of the rapid modeling method. Full article
(This article belongs to the Section Acoustics and Vibrations)
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35 pages, 11915 KB  
Article
Interactive Experience Design for the Historic Centre of Macau: A Serious Game-Based Study
by Pengcheng Zhao, Pohsun Wang, Yi Lu, Yao Lu and Zi Wang
Buildings 2026, 16(2), 323; https://doi.org/10.3390/buildings16020323 - 12 Jan 2026
Viewed by 162
Abstract
With the advancement of digital technology, serious games have become an essential tool for disseminating and educating individuals about cultural heritage. However, systematic empirical research remains limited with respect to how visual elements influence users’ cognitive and emotional engagement through interactive behaviors. Using [...] Read more.
With the advancement of digital technology, serious games have become an essential tool for disseminating and educating individuals about cultural heritage. However, systematic empirical research remains limited with respect to how visual elements influence users’ cognitive and emotional engagement through interactive behaviors. Using the “Macau Historic Centre Science Popularization System” as a case study, this mixed-methods study investigates the mechanisms by which visual elements affect user experience and learning outcomes in digital interactive environments. Eye-tracking data, behavioral logs, questionnaires, and semi-structured interviews from 30 participants were collected to examine the impact of visual elements on cognitive resource allocation and emotional engagement. The results indicate that the game intervention significantly enhanced participants’ retention and comprehension of cultural knowledge. Eye-tracking data showed that props, text boxes, historic buildings, and the architectural light and shadow shows (as incentive feedback elements) had the highest total fixation duration (TFD) and fixation count (FC). Active-interaction visual elements showed a stronger association with emotional arousal and were more likely to elicit high-arousal experiences than passive-interaction elements. The FC of architectural light and shadow shows a positive correlation with positive emotions, immersion, and a sense of accomplishment. Interview findings revealed users’ subjective experiences regarding visual design and narrative immersion. This study proposes an integrated analytical framework linking “visual elements–interaction behaviors–cognition–emotion.” By combining eye-tracking and information dynamics analysis, it enables multidimensional measurement of users’ cognitive processes and emotional responses, providing empirical evidence to inform visual design, interaction mechanisms, and incentive strategies in serious games for cultural heritage. Full article
(This article belongs to the Special Issue New Challenges in Digital City Planning)
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24 pages, 10601 KB  
Article
Measurement and Simulation Analysis of Noise and Vibration in a Combine Harvester Cab Based on Pivot Noise Transfer Function and Vibroacoustic Coupling Method
by Kuizhou Ji, Yaoming Li, Yanbin Liu and Hanhao Wang
Machines 2026, 14(1), 90; https://doi.org/10.3390/machines14010090 - 12 Jan 2026
Viewed by 107
Abstract
To address the pronounced issue of noise and vibration within the combine harvester cab, this study proposes a hybrid simulation and experimental validation approach that integrates the pivot noise transfer function (NTF) with a finite element method (FEM)-based vibroacoustic coupling analysis. A coupled [...] Read more.
To address the pronounced issue of noise and vibration within the combine harvester cab, this study proposes a hybrid simulation and experimental validation approach that integrates the pivot noise transfer function (NTF) with a finite element method (FEM)-based vibroacoustic coupling analysis. A coupled finite element model combining the cab structure and its internal acoustic cavity was developed, with the excitation path characteristics explicitly defined. The coupled interaction between structural and acoustic modes, along with its influence on noise transmission, was systematically examined. The analysis revealed a significant transmission peak near 18 Hz at critical pivot Point D under specific excitation directions, indicating strong directional sensitivity in the excitation–response relationship. Experimental validation showed that the discrepancy between simulated and measured responses, including the NTFs, remained within 15%, confirming the accuracy and applicability of the proposed method. This research offers a reliable analytical framework and practical reference for noise and vibration reduction in agricultural machinery cab design. Full article
(This article belongs to the Special Issue Advances in Noise and Vibrations for Machines: Second Edition)
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40 pages, 4234 KB  
Review
Advances in Analytical Methods for Quality Control and Authentication of Nutraceuticals: A Comprehensive Review
by Gergana Kirilova Kirova
Nutraceuticals 2026, 6(1), 5; https://doi.org/10.3390/nutraceuticals6010005 - 12 Jan 2026
Viewed by 206
Abstract
Nutraceuticals are food-based products that provide health benefits beyond basic nutrition and play an increasingly important role in preventive healthcare. Ensuring their quality, safety, and efficacy is critical as the global market expands. A systematic literature search was conducted in Scopus, Web of [...] Read more.
Nutraceuticals are food-based products that provide health benefits beyond basic nutrition and play an increasingly important role in preventive healthcare. Ensuring their quality, safety, and efficacy is critical as the global market expands. A systematic literature search was conducted in Scopus, Web of Science, and PubMed using keywords such as ‘nutraceuticals,’ functional foods,’ and ‘quality control,’ with studies selected based on their focus on methods for standardization, characterization, and quality assessment. This review summarizes current analytical approaches, including spectroscopic, chromatographic, and techniques for elemental analysis, highlighting their applications in compound identification, quantification, detection of adulterants, and overall quality control. Emerging challenges and future trends, such as the integration of chemometrics and real-time analytical strategies, are also discussed, providing a comprehensive perspective on the evolving field of nutraceutical analysis. Full article
(This article belongs to the Special Issue Feature Review Papers in Nutraceuticals)
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21 pages, 83627 KB  
Article
Research on Urban Perception of Zhengzhou City Based on Interpretable Machine Learning
by Mengjing Zhang, Chen Pan, Xiaohua Huang, Lujia Zhang and Mengshun Lee
Buildings 2026, 16(2), 314; https://doi.org/10.3390/buildings16020314 - 11 Jan 2026
Viewed by 124
Abstract
Urban perception research has long focused on global metropolises, but has overlooked many cities with complex functions and spatial structures, resulting in insufficient universality of existing theories when facing diverse urban contexts. This study constructed an analytical framework that integrates street scene images [...] Read more.
Urban perception research has long focused on global metropolises, but has overlooked many cities with complex functions and spatial structures, resulting in insufficient universality of existing theories when facing diverse urban contexts. This study constructed an analytical framework that integrates street scene images and interpretable machine learning. Taking Zhengzhou City as the research object, it extracted street visual elements based on deep learning technology and systematically analyzed the formation mechanism of multi-dimensional urban perception by combining the LightGBM model and SHAP method. The main findings of the research are as follows: (1) The urban perception of Zhengzhou City shows a significant east–west difference with Zhongzhou Avenue as the boundary. Positive perceptions such as safety and vitality are concentrated in the central business district and historical districts, while negative perceptions are more common in the urban fringe areas with chaotic built environments and single functions. (2) The visibility of greenery, the openness of the sky and the continuity of the building interface are identified as key visual elements affecting perception, and their directions and intensifies of action show significant differences due to different perception dimensions. (3) The influence of visual elements on perception has a complex mechanism of action. For instance, the promoting effect of greenery visibility on beauty perception tends to level off after reaching a certain threshold. The research results of this study can provide quantitative basis and strategic reference for the improvement in urban space quality and humanized street design. Full article
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20 pages, 3748 KB  
Article
Exploring Environmental Element Monitoring Data Using Chemometric Techniques: A Practical Case Study from the Tremiti Islands (Italy)
by Raffaele Emanuele Russo, Martina Fattobene, Silvia Zamponi, Paolo Conti, Ana Herrero and Mario Berrettoni
Molecules 2026, 31(2), 232; https://doi.org/10.3390/molecules31020232 - 9 Jan 2026
Viewed by 230
Abstract
Environmental element monitoring is essential for assessing environmental quality, identifying pollution sources, evaluating ecological risks, and understanding long-term contamination trends. Modern monitoring campaigns routinely generate large volumes of complex data that require advanced analytical strategies. This study applied chemometric techniques to analyze elements [...] Read more.
Environmental element monitoring is essential for assessing environmental quality, identifying pollution sources, evaluating ecological risks, and understanding long-term contamination trends. Modern monitoring campaigns routinely generate large volumes of complex data that require advanced analytical strategies. This study applied chemometric techniques to analyze elements and BVOCs (biogenic volatile organic compounds) measured from Posidonia oceanica and related environmental matrices (seawater, sediment, and rhizomes) during three sampling campaigns in the Tremiti Islands (Italy). Twenty-two trace elements were quantified, and BVOC profiles were obtained from the leaf samples. The dataset was analyzed using a combination of univariate visualizations, unsupervised and supervised multivariate techniques, and multi-way methods. PCA (Principal Component Analysis) and PLS-DA (Partial Least Squares-Discriminant Analysis) revealed distinct spatial (leaf section) and temporal (sampling period) trends, supported by consistent elemental markers. A low-level data fusion approach integrating BVOC and element data improved group discrimination and interpretability. PARAFAC (PARAllel FACtor analysis) applied to a three-way array successfully separated background trends from meaningful compositional changes, uncovering latent structures across chemical, spatial, and temporal dimensions. This work illustrates the usefulness of chemometrics in environmental monitoring and the effectiveness of combining multivariate tools and data fusion to improve the interpretability of complex environmental datasets. The methodology used in this study is fully generalizable and applicable to other environmental multi-way datasets. Full article
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18 pages, 3200 KB  
Article
Non-Circular Domain Surface Figure Analysis of High-Dynamic Scanning Mirrors Under Multi-Physics Coupling
by Xiaoyan He, Kaiyu Jiang, Penglin Liu, Xi He and Peng Xie
Photonics 2026, 13(1), 65; https://doi.org/10.3390/photonics13010065 - 9 Jan 2026
Viewed by 191
Abstract
The use of large-aperture scanning mirrors for high-resolution and wide-swath imaging represents a major trend in Earth observation technology. However, to improve dynamic response performance, scanning mirror assemblies are highly lightweighted, resulting in reduced overall stiffness. This makes the mirror surface susceptible to [...] Read more.
The use of large-aperture scanning mirrors for high-resolution and wide-swath imaging represents a major trend in Earth observation technology. However, to improve dynamic response performance, scanning mirror assemblies are highly lightweighted, resulting in reduced overall stiffness. This makes the mirror surface susceptible to thermal and inertial loads during operation, leading to degraded surface accuracy and poor imaging quality. Moreover, dynamic scanning mirror has the multi-disciplinary coupling effects and non-circular structural characteristics. It poses significant challenges for surface figure analysis. To address these issues, this paper proposes a surface analysis method for high-dynamic scanning mirrors under multi-physics coupling in non-circular domains. First, a finite element model of the mirror assembly is established based on the minimum aperture and angular velocity parameters. Through finite element analysis, the surface response of the scanning mirror assembly under thermal loads, dynamic inertial loads, and their coupled effects is quantitatively investigated. Subsequently, an analytical approach, which combines rigid-body displacement separation and Gram–Schmidt orthogonalization, is developed to construct non-circular Zernike polynomials, enabling high-precision fitting and reconstruction of the mirror’s dynamic surface distortions. Numerical experiments validate the accuracy of the model. Results show that for a scanning mirror with an aperture of 466 mm × 250 mm under the coupled condition of a 5 °C temperature rise and 50 N·mm torque, the surface figure achieves RMS < 2 nm and PV < 22 nm, with a fitting accuracy achieves 10−6. These results verify the accuracy and reliability of the proposed method. The surface analysis approach presented in this study provides theoretical guidance and a design framework for subsequent image quality evaluation and assurance. Full article
(This article belongs to the Special Issue Advances in Optical Precision Manufacturing and Processing)
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17 pages, 4208 KB  
Article
Equivalent Elastic Modulus Study of a Novel Quadrangular Star-Shaped Zero Poisson’s Ratio Honeycomb Structure
by Aling Luo, Dong Yan, Zewei Wu, Hong Lu and He Ling
Symmetry 2026, 18(1), 127; https://doi.org/10.3390/sym18010127 - 9 Jan 2026
Viewed by 225
Abstract
This study proposes a novel four-pointed-star-shaped honeycomb structure having zero Poisson’s ratio, designed to overcome the stress concentration inherent in traditional point-to-point connected star-shaped honeycombs.By introducing a horizontal connecting wall at cell junctions, the new configuration achieves a more uniform stress distribution and [...] Read more.
This study proposes a novel four-pointed-star-shaped honeycomb structure having zero Poisson’s ratio, designed to overcome the stress concentration inherent in traditional point-to-point connected star-shaped honeycombs.By introducing a horizontal connecting wall at cell junctions, the new configuration achieves a more uniform stress distribution and enhanced structural stability. An analytical model for the in-plane equivalent elastic modulus was derived using homogenization theory and the energy method. The model, along with the structure’s zero Poisson’s ratio characteristic, was validated through finite element simulations and experimental compression tests. The simulations predicted an equivalent elastic modulus of 51.71 MPa (Y-direction) and 74.67 MPa (X-direction), which aligned closely with the experimental measurements of 56.61 MPa and 60.50 MPa, respectively. The experimental Poisson’s ratio was maintained near zero (v = 0.02). Parametric analysis further revealed that the in-plane equivalent elastic modulus decreases with increases in the wall angle, horizontal wall length, and wall thickness. This work demonstrates a successful structural optimization strategy that improves both mechanical performance and manufacturability for zero Poisson’s ratio honeycomb applications. Full article
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