International Journal of Mechanical Sciences最新文献

{"title":"Tension and torsion distributions in tapered threaded connections","authors":"Tengfei Shi ,&nbsp;Zeyu Qi ,&nbsp;Caishan Liu ,&nbsp;Xiangyu Li","doi":"10.1016/j.ijmecsci.2025.110135","DOIUrl":"10.1016/j.ijmecsci.2025.110135","url":null,"abstract":"<div><div>Tapered threaded connections are widely used in casing and tubing applications. The load distribution in these connections is crucial for their strength and sealing performance. In this paper, we develop a tension–torsion coupling model for tapered thread connections for the first time. In the proposed model, the main structures of the connections are described as tension–torsion bars with variable properties, while the threads are modeled as modified cantilever beams fixed on the bars. By introducing the compatibility conditions and constitutive relations for thread contact, the contact force can be analytically obtained, and the tension–torsion coupling equilibrium equations for the connection are derived. The validation of the proposed model is confirmed through finite element analysis. While the finite element simulations require more than 1.6 h, the proposed model can instantaneously provide the load distributions. Based on the proposed model, the influence of geometrical and material parameters on load distribution is investigated. The comprehensive simulations demonstrate that the maximum tension and torsion loads are located at the cross-section where the external load is applied and where the connection is fixed. As the tapered angle increases and the thread angle decreases, both the maximum contact force and torque increase. The results obtained from the proposed model provide valuable insights for the design of sealing mechanisms in casing and tubing applications.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"291 ","pages":"Article 110135"},"PeriodicalIF":7.1,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comprehensive thermoelastic stress-driven approach for thermo-mechanical-pressure multiphysics systems","authors":"Thanh T. Banh,&nbsp;Dongkyu Lee","doi":"10.1016/j.ijmecsci.2025.110133","DOIUrl":"10.1016/j.ijmecsci.2025.110133","url":null,"abstract":"<div><div>In the design of multiphysics systems, particularly in aerospace, automotive, and civil engineering, optimizing stress distribution is crucial for ensuring the longevity and safety of structures. This study proposes a comprehensive methodology to address stress-related challenges in multiphysics systems, essential for maintaining structural integrity under complex thermo-mechanical-pressure loading conditions. The proposed methodology provides three principal contributions: (i) a novel solution for stress-related problems involving design-dependent pressure loads, achieved by establishing a design-dependent pressure field using Darcy’s law and a drainage term to implicitly identify pressure-bounding surfaces, providing an efficient method for evaluating load sensitivities; (ii) a comprehensive thermoelastic stress methodology for thermo-mechanical-pressure systems; and (iii) an extension to multiple material candidates to enhance robustness and design flexibility. To achieve these objectives, the well-established <span><math><mi>P</mi></math></span>-norm approach is employed to consolidate stresses into a unified global metric, while clustered regional and adaptive scaling techniques are used to manage localized stress concentrations effectively. The Moved and Regularized Heaviside function (MRHF)-based stress interpolation is integrated within the generalized Solid Isotropic Material with Penalization (SIMP) framework to handle multi-material problems efficiently. Furthermore, three adjoint vectors are introduced for thermoelastic stress sensitivity analysis using the adjoint variable technique, improving computational efficiency alongside a polygonal discretization scheme that enhances adaptability with diverse element types. The methodology’s efficiency, robustness, and practicality are demonstrated through various numerical examples, showing significant improvements in stress distribution and overall multiphysics system performance. Validation and verification processes further confirm the approach’s effectiveness, while numerical results highlight the influence of heat flux magnitude and material selection on optimized outcomes, demonstrating the methodology’s versatility for both stress minimization and stress-constrained problems. These contributions advance the field of multiphysics topology optimization by offering practical, robust, and efficient solutions to complex engineering challenges, providing a solid foundation for future developments in complex systems.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"291 ","pages":"Article 110133"},"PeriodicalIF":7.1,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Composite-airfoil-plate with embedded macro-fiber-composites: Aero-thermo-electro vibration analysis and active control","authors":"Yu Zhang ,&nbsp;Hui Zhang ,&nbsp;Hongwei Ma ,&nbsp;Wei Sun ,&nbsp;Kunpeng Xu ,&nbsp;Hui Li","doi":"10.1016/j.ijmecsci.2025.110143","DOIUrl":"10.1016/j.ijmecsci.2025.110143","url":null,"abstract":"<div><div>With the rapid development of aerospace technology, fiber reinforced composites (FRCs) have been widely used because of their excellent mechanical properties, especially composite airfoil plates with non-rectangular geometric characteristics (CAPs-NRG). Aiming at the complex vibration behavior of these structures, which may be caused by aerodynamic pressure and thermal load in high altitude and supersonic environments, a novel active vibration control design scheme of embedded macro fiber composites (MFCs) is proposed in this paper. Firstly, a dynamic modeling method of aero-thermo-electro coupling based on the penalty function method is developed to describe the dynamic response of CAPs-NRG with embedded MFCs accurately. The rationality of the model is verified by comparing it with the literature and the finite element method. Secondly, to deal with the adverse effects of complex aerodynamic loads and environmental noise on control performance, an adaptive hybrid control algorithm of the filtered-proportional differential-linear quadratic regulator (F-PD-LQR) based on the power change is designed to achieve more precise and reliable vibration control. Furthermore, the influence of geometric parameters of CAPs-NRG on flutter behavior is discussed, and the effectiveness of the proposed control algorithm under different aerodynamic pressure and temperature conditions is evaluated. Through the above research, this paper provides an efficient and reliable flutter control solution for CAPs-NRG and lays a foundation for ensuring flight vehicle safety.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"290 ","pages":"Article 110143"},"PeriodicalIF":7.1,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dual Hamiltonian transformation and magneto-electro-thermo-viscoelastic contact analysis","authors":"Lizichen Chen ,&nbsp;C.W. Lim ,&nbsp;Weiqiu Chen","doi":"10.1016/j.ijmecsci.2025.110077","DOIUrl":"10.1016/j.ijmecsci.2025.110077","url":null,"abstract":"<div><div>The application of high-throughput testing methodologies and the involvement of functionally graded specimens for material characterization show immense potential and plays an indispensable role in the progressive advent of advanced materials. Nevertheless, the inherent material inhomogeneity and multi-field coupling pose great obstacles in the fundamental theory and analysis for the behavior of functionally graded specimens, thus necessitating the proposal of new and innovative analytical approaches. Here, the contact model and analysis of a finite-sized magneto-electro-thermo-viscoelastic plane with a horizontal exponential material gradient is established based on a new symplectic approach. With prior linearization via Laplace transform, the state equations are constructed in the matrix form, resulting in the dual Hamiltonian transformation under homogeneous displacement constraint. The dual adjoint symplectic orthogonality is introduced and proved, elucidating the implications of symmetry breaking. General and particular solutions are derived to constitute the complete solution in the symplectic expansion. The analytical solution is verified by comparing with highly precise finite element solutions in the entire domain. This current work not only paves the way for an efficient and robust analytical framework via the symplectic methodology, but also sets a foundation with benchmark exact solutions for future research endeavors.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"290 ","pages":"Article 110077"},"PeriodicalIF":7.1,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamically consistent phase-field modeling of elastocaloric effect: Indirect vs direct method","authors":"Wei Tang ,&nbsp;Qihua Gong ,&nbsp;Min Yi ,&nbsp;Bai-Xiang Xu","doi":"10.1016/j.ijmecsci.2025.110134","DOIUrl":"10.1016/j.ijmecsci.2025.110134","url":null,"abstract":"<div><div>Modeling elastocaloric effect (eCE) is crucial for the design of environmentally friendly and energy-efficient eCE based solid-state cooling devices. Here, a thermodynamically consistent non-isothermal phase-field model (PFM) coupling martensitic transformation with mechanics and heat transfer is developed and applied for simulating eCE. The model is derived from a thermodynamic framework which invokes the microforce theory and Coleman–Noll procedure. To avoid the numerical issue related to the non-differentiable energy barrier function across the transition point, the austenite–martensite transition energy barrier in PFM is constructed as a smooth function of temperature. Both the indirect method using isothermal PFM with Maxwell relations and the direct method using non-isothermal PFM are applied to calculate the elastocaloric properties. The former is capable of calculating both isothermal entropy change and adiabatic temperature change (<span><math><mrow><mi>Δ</mi><msub><mrow><mi>T</mi></mrow><mrow><mtext>ad</mtext></mrow></msub></mrow></math></span>), but induces high computation cost. The latter is computationally efficient, but only yields <span><math><mrow><mi>Δ</mi><msub><mrow><mi>T</mi></mrow><mrow><mtext>ad</mtext></mrow></msub></mrow></math></span>. In a model Mn–22Cu alloy, the maximum <span><math><mrow><mi>Δ</mi><msub><mrow><mi>T</mi></mrow><mrow><mtext>ad</mtext></mrow></msub></mrow></math></span> (<span><math><mrow><mi>Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mtext>ad</mtext></mrow><mrow><mtext>max</mtext></mrow></msubsup></mrow></math></span>) under a compressive stress of 100 MPa is calculated as 9.5 and 8.5 K in single crystal (3.5 and 3.8 K in polycrystal) from the indirect and direct method, respectively. It is found that the discrepancy of <span><math><mrow><mi>Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mtext>ad</mtext></mrow><mrow><mtext>max</mtext></mrow></msubsup></mrow></math></span> by indirect and direct method is within 10% at stress less than 150 MPa, confirming the feasibility of both methods in evaluating eCE at low stress. However, at higher stress, <span><math><mrow><mi>Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mtext>ad</mtext></mrow><mrow><mtext>max</mtext></mrow></msubsup></mrow></math></span> obtained from the indirect method is notably larger than that from the direct one. This is mainly attributed to that in the non-isothermal PFM simulations, the relatively large temperature increase at high stress could in turn hamper the austenite–martensite transition and thus finally yield a lower <span><math><mrow><mi>Δ</mi><msub><mrow><mi>T</mi></mrow><mrow><mtext>ad</mtext></mrow></msub></mrow></math></span>. The results demonstrate the developed PFM herein, combined with both indirect and direct method for eCE calculations, as a practicable toolkit for the computational design of elastocaloric devices.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"291 ","pages":"Article 110134"},"PeriodicalIF":7.1,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shock compression and spallation of polyamides 6 and 66","authors":"R.C. Pan ,&nbsp;B.X. Bie ,&nbsp;Y. Cai ,&nbsp;N.B. Zhang ,&nbsp;L.Z. Chen ,&nbsp;Y.X. Zhao ,&nbsp;K. Li ,&nbsp;H.W. Chai ,&nbsp;L. Lu ,&nbsp;S.N. Luo","doi":"10.1016/j.ijmecsci.2025.110127","DOIUrl":"10.1016/j.ijmecsci.2025.110127","url":null,"abstract":"<div><div>Polyamide 6 (PA6) and polyamide 66 (PA66) are widely used engineering polymers for high-speed applications, and yet their behaviors under extreme impact loading remain unclear. We systematically investigate their dynamic responses through plate impact experiments, and measure their Hugoniot equations of state (shock adiabats) and free-surface velocity histories up to peak shock stress of <span><math><mo>∼</mo></math></span>1.6 GPa. The postmortem samples are characterized with synchrotron X-ray computed tomography. Quadratic and linear shock velocity–particle velocity relations are obtained for PA6 and PA66, respectively. Spall strength remains nearly constant for both PA6 and PA66 (approximately 0.18 GPa and 0.23 GPa, respectively) up to peak shock stress of 1.1 GPa. PA6 and PA66 demonstrate ductile and brittle fracture characteristics under high strain rate tension, respectively. The influences of chain conformations and hydrogen bond density on the dynamic mechanical properties and underlying damage mechanisms are elucidated. These differences in dynamic responses of PA6 and PA66 can be attributed to rearrangement and breakage of polymer chains, significantly influenced by varying hydrogen bond frequencies. This study contributes to understanding the connections between hydrogen bond density, chain conformation, and bulk mechanical properties in polyamides, and can be useful for advancing their applications in protective and structural materials.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"291 ","pages":"Article 110127"},"PeriodicalIF":7.1,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of leakage flow on sediment erosion in guide vane region","authors":"Zilong Zhao ,&nbsp;Zhongdong Qian ,&nbsp;Ole Gunnar Dahlhaug ,&nbsp;Zhiwei Guo","doi":"10.1016/j.ijmecsci.2025.110122","DOIUrl":"10.1016/j.ijmecsci.2025.110122","url":null,"abstract":"<div><div>The erosion of hydraulic turbine components in sediment-laden flows poses considerable operational and maintenance challenges in hydroelectric power generation. The current work is aimed at investigating the sediment erosion of a guide vane (GV), a head cover, and a shaft located within the GV region of a Francis turbine, particularly focusing on the effects of leakage flow. An Euler–Lagrange numerical method is used to predict erosion. Specifically, erosion-induced deformation is also considered by using a dynamic mesh. The distribution and intensity of erosion in the GV region, along with the erosion mechanisms associated with leakage flow, are thoroughly examined. Additionally, the impact of erosion-induced deformation on the flow pattern and erosion itself is analyzed. The results indicate that the head cover, as well as the leading edge of the GV and the shaft, sustains considerable erosive damage. Notably, erosion of the head cover is particularly severe and is exacerbated by increases in the mass flow rate or particle size. The leakage vortex, formed by the interaction of the leakage flow with the main flow in the GV region, is responsible for the severe erosion observed on the head cover. This leakage vortex attracts particles, which repeatedly impact the head cover at high speeds. Furthermore, these particle impacts lead to localized erosion-induced deformation, resulting in pit formation. The presence of the pit alters the flow characteristics near the wall region, causing more particles to collide with the pit and ultimately accelerating the erosion process.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"291 ","pages":"Article 110122"},"PeriodicalIF":7.1,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Indentation of freestanding pre-stressed films: Extracting elastic modulus and pre-tension, elucidating finite-sized indenter effect","authors":"Shuyi Xiang ,&nbsp;Longkun Lu ,&nbsp;Zhibo Du ,&nbsp;Kaijie Wang ,&nbsp;Zhanli Liu","doi":"10.1016/j.ijmecsci.2025.110141","DOIUrl":"10.1016/j.ijmecsci.2025.110141","url":null,"abstract":"<div><div>The indentation test is an important method for characterizing the mechanical properties of solid films. However, how to extract the elastic modulus of pre-stressed circular films through the indentation test is still debatable due to the transition between linear membrane, nonlinear membrane, and plate behavior. This study proposes a method for extracting elastic modulus and pre-tension of freestanding film simultaneously by integrating an indentation test and theoretical modeling. Firstly, we introduce the experimental setting and results of polydimethylsiloxane (PDMS) films. The theoretical model for the cylindrical indentation of freestanding circular film is then presented, considering the combined contribution of pre-tension, additional stretching, and bending stiffness to mechanical response. After that, the elastic modulus and pre-tension are extracted by iteratively solving the full governing equations until the difference between numerical and experimental load-deflection curves is minimized. The asymptotic results derived from the full governing equations are compared with classical asymptotic solutions in the linear membrane, nonlinear membrane, and plate regimes to verify the theoretical modeling. Finally, the explicit indentation force-depth formula for the finite-sized indenter is proposed. The underlying mechanism of the synergistic effect of pre-tension, additional stretching and bending stiffness on indentation behavior in the transition region is elucidated.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"291 ","pages":"Article 110141"},"PeriodicalIF":7.1,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite deformations induce friction hysteresis in normal wavy contacts","authors":"M. Ceglie,&nbsp;G. Violano,&nbsp;L. Afferrante,&nbsp;N. Menga","doi":"10.1016/j.ijmecsci.2025.110115","DOIUrl":"10.1016/j.ijmecsci.2025.110115","url":null,"abstract":"<div><div>Since Hertz’s pioneering work in 1882, contact mechanics has traditionally been grounded in linear elasticity, assuming small strains and displacements. However, recent experiments clearly highlighted linear elasticity limitations in accurately predicting the contact behavior of rubbers and elastomers, particularly during frictional slip, which is governed by geometric and material nonlinearity.</div><div>In this study, we investigate the basic scenario involving normal approach-retraction contact cycles between a wavy rigid indenter and a flat, deformable substrate. Both frictionless and frictional interfacial conditions are examined, considering finite strains, displacements, and nonlinear rheology. We developed a finite element model for this purpose and compared our numerical results with Westergaard’s linear theory.</div><div>Our findings show that, even in frictionless conditions, the contact response is significantly influenced by geometric and material nonlinearity, particularly for wavy indenters with high aspect ratios, where normal-tangential stresses and displacements coupling emerges. More importantly, interfacial friction in nonlinear elasticity leads to contact hysteresis (i.e., frictional energy dissipation) during normal loading–unloading cycles. This behavior cannot be explained in a linear framework; therefore, most of the experiments reporting hysteresis are typically explained invoking other interfacial phenomena (e.g., adhesion, plasticity, or viscoelasticity). Here we present an additional suitable explanation relying on finite strains/displacements with detailed peculiarities, such as vanishing pull-off force. Moreover, we also report an increase of hysteretic losses as for confined systems, stemming from the enhanced normal-tangential nonlinear coupling.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"291 ","pages":"Article 110115"},"PeriodicalIF":7.1,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A physics-informed neural network-based method for dispersion calculations","authors":"Zhibao Cheng ,&nbsp;Tianxiang Yu ,&nbsp;Gaofeng Jia ,&nbsp;Zhifei Shi","doi":"10.1016/j.ijmecsci.2025.110111","DOIUrl":"10.1016/j.ijmecsci.2025.110111","url":null,"abstract":"<div><div>The study of dispersion relations of periodic structures or elastic metamaterials is essential to understand and optimize their unique wave propagation characteristics. By integrating physical laws for the generation of physically consistent results without labeled data, Physics-Informed Neural Networks (PINNs) offer a new perspective on scientific computation, which is a potential machine learning method in advancing the analysis and design of advanced materials. In this study, we introduce a novel PINN-based numerical method for the calculation of dispersion calculations of periodic structures. First, coupling the physical information of the dispersion problem of periodic structures and the neural networks PDE solver, the framework of the proposed method is constructed. Unlike those existing PINNs, the proposed PINN is designed for the first time to handle the dispersion problem as well as the equivalent eigenvalue problem. In particular, a unified framework is proposed to solve both the real and complex eigenvalue problems, from which the real and complex dispersion curves of periodic structures are obtained. Second, comparing with the analytical results, the correctness of the proposed method is validated. And, dispersion properties for propagative waves in pass bands and evanescent waves in stop bands are analyzed. Third, a comprehensive analysis of the convergence of the proposed method is performed. The Neural Tangent Kernel (NTK)-based adaptive loss weighting scheme is integrated into the proposed PINN to achieve the balanced convergence across different loss terms. Meanwhile, the Random Fourier Feature Mapping is implemented into the proposed method to mitigate the eigenfrequency bias problem. Comparison results demonstrate that such enhancements allow for a more accurate convergence. For the considered dispersion problem, a coherent convergence is achieved for all eigenfrequencies in the desired frequency range. In summary, the proposed physics-informed machine learning method is a promising computational method for the dispersion problem of periodic structures.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"291 ","pages":"Article 110111"},"PeriodicalIF":7.1,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}