Acta Mechanica最新文献

{"title":"Modeling and evaluation of multilayer coating effects on the thermal behavior of semi-infinite solids","authors":"Roman Kulchytsky-Zhyhailo,&nbsp;Yuriy Tokovyy","doi":"10.1007/s00707-026-04733-2","DOIUrl":"10.1007/s00707-026-04733-2","url":null,"abstract":"<div><p>This study proposes a method for assessing the applicability of the homogenization model with microlocal parameters in determining the thermophysical properties of multilayer coatings constructed from representative cells consisting of two homogeneous isotropic materials. The investigation is based on solving a two-dimensional quasi-steady-state heat conduction problem for a semi-infinite solid with an insulation coating subjected to a moving heat source. Two models are considered for the coating analysis: one that accounts for the actual layered structure of the coating and another that represents a homogenized coating with continuously varying properties. The solutions are constructed using the Fourier integral transform and two different approaches for approximating the homogenized coating, i.e., by substituting it with a set of homogeneous transversely isotropic layers, and by constructing an approximate solution with modeling functions. It is shown that both approaches ensure a high level of accuracy for specific geomerties, while the latter one is more efficient computationally. Conditions under which the homogenized model adequately simulates the actual layered structure are frameworked. In particular, when the ratio of the representative cell thickness to the heating area width is below 10⁻², the homogenized model provides results acceptable for engineering applications. The approach also enables the correct estimation of local heat fluxes within individual components of the coating, enhancing thereby its applicability for modeling real gradient coatings in thermomechanical analyses.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5149 - 5167"},"PeriodicalIF":4.0,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149188995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 fractional Green–Lindsay magneto-thermo-viscoelastic model with dual-relaxation times for perfect conductors","authors":"Mohamed H. Hendy,&nbsp;Magdy A. Ezzat","doi":"10.1007/s00707-026-04764-9","DOIUrl":"10.1007/s00707-026-04764-9","url":null,"abstract":"<div><p>This work develops a fractional Green–Lindsay magneto-thermo-viscoelastic model with dual-relaxation times for perfectly conducting materials. The motivation of this study is to describe hereditary and memory-dependent thermomechanical behavior in advanced viscoelastic materials that cannot be captured by classical integer-order models. Although Green–Lindsay theory introduces finite-speed heat propagation through dual-relaxation times, it does not include fractional hereditary effects in the constitutive relations. Existing fractional models usually treat thermal relaxation and viscoelastic memory separately. The novelty of the present work is the development of a unified framework that combines dual thermal relaxation, fractional rheological operators, and electromagnetic coupling in a single model. The governing equations are solved analytically in the Laplace transform domain for a one-dimensional thermal-shock problem, and numerical inversion is used to obtain the field distributions. Numerical results for polymethyl methacrylate (PMMA) show that the fractional parameters significantly affect thermal propagation, stress attenuation, and electromagnetic response. The results confirm that the proposed model provides stronger damping and more realistic memory-dependent behavior compared with classical thermoelastic models.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5129 - 5147"},"PeriodicalIF":4.0,"publicationDate":"2026-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vibration transmission bandgap analysis of porous functionally graded periodic beams in thermal environment using the wave-based approach","authors":"Dongze He,&nbsp;Shuai Wang,&nbsp;Shuang Du","doi":"10.1007/s00707-026-04771-w","DOIUrl":"10.1007/s00707-026-04771-w","url":null,"abstract":"<div><p>Porous functionally graded materials (FGMs) have attracted considerable attention in advanced engineering structures due to their lightweight characteristics and tunable mechanical properties. In this study, the vibration characteristics of porous functionally graded periodic beam structures under thermal environments are investigated using the wave-based analytical framework. Based on the Timoshenko beam theory, the displacement field is expressed in the form of wave functions, and the displacement and force parameter matrices for beam elements are derived. By imposing the continuity conditions between adjacent elements, the global formulation for periodic beam structures is established, enabling efficient calculation of the frequency response functions. The accuracy of the proposed model is validated through comparisons with finite element results, showing excellent agreement. On this basis, the vibration transmission characteristics of porous functionally graded periodic beams are systematically analyzed. Parametric studies are conducted to examine the effects of temperature variation, porosity coefficient, gradient index, and geometric parameters on the frequency response and vibration transmission bandgaps. Unlike previous studies that primarily focus on either homogeneous periodic structures or non-periodic porous functionally graded beams under isothermal conditions, the present work establishes a unified wave-based framework for analyzing vibration transmission in porous functionally graded periodic beams with temperature-dependent material properties. The combined effects of periodicity, material gradation, porosity, and thermal loading on bandgap characteristics are systematically revealed, providing new insights for the design of lightweight structures with enhanced vibration attenuation performance.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5085 - 5104"},"PeriodicalIF":4.0,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of angle misalignment error and center distance deviation on time-varying mesh stiffness of a spur gear pair","authors":"Guang Chen,&nbsp;Wei Li,&nbsp;Jie Zhang,&nbsp;Manxian Liu","doi":"10.1007/s00707-026-04766-7","DOIUrl":"10.1007/s00707-026-04766-7","url":null,"abstract":"<div><p>Angle misalignment error and center distance deviation are inevitable imperfections in gear transmission systems. These two faults frequently coexist, directly affecting the time-varying mesh stiffness (TVMS) and, consequently, the vibrational response of the gear system. Establishing a gear TVMS model that accounts for the coupling effect between angle misalignment error and center distance deviation is crucial for the early design and subsequent fault diagnosis of gear transmission systems. This paper establishes a gear TVMS model that accounts for the coupling between angle misalignment error and center distance deviation. The accuracy of the proposed model is validated through finite element simulations. Using the proposed stiffness model, we investigate the respective influence of each individual fault on the meshing stiffness. The variation trend of meshing stiffness with backup ratio under fault conditions is quantitatively analyzed, and a design strategy is proposed—setting the backup ratio between 2.5 and 3.5—to mitigate the effects of these faults. A comparative study was conducted on the influences of the coupled fault and the individual single faults on the mesh stiffness. The results show that the influence of the coupled fault on the meshing stiffness of the system is manifested as a nonlinear combination of the influences of single faults. Furthermore, this nonlinear characteristic becomes more pronounced as the severity of the faults increases. In the case study in this paper, the difference between them reaches 18.71%. This study provides a theoretical foundation for optimizing the design and fault diagnosis of gear transmission systems.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5055 - 5083"},"PeriodicalIF":4.0,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear free vibration of magneto–electro–elastic sandwich plates with auxetic cores under coupled thermo–electro–magnetic fields","authors":"Ismail Esen,&nbsp;Seyit Ali Kara","doi":"10.1007/s00707-026-04763-w","DOIUrl":"10.1007/s00707-026-04763-w","url":null,"abstract":"<div><p>This study presents a comprehensive nonlinear vibration analysis of magneto–electro–elastic (MEE) sandwich plates incorporating auxetic core architectures under coupled thermo–electro–magnetic fields. A semi-analytical formulation based on higher-order shear deformation theory (HSDT) and nonlocal strain-gradient theory is developed to capture geometric nonlinearity, size dependency, and multi-field coupling effects. Finite element analysis is employed only at the unit-cell level to homogenize the effective elastic properties of the anti-tetrachiral auxetic core. The results reveal that increasing the auxetic core thickness ratio leads to a reduction of the fundamental normalized frequency by approximately 15–35%, depending on the geometric configuration, due to enhanced internal rotational mechanisms and reduced effective bending stiffness. Thermal loading is found to have a dominant influence on the dynamic response, causing a continuous decrease in frequency and leading to a critical minimum at Δ<i>T</i> ≈ 2000 K, where the frequency drops by nearly 40–60% compared to the initial state. This temperature level may be interpreted as a critical-like thermally dominated transition region, where thermally induced compressive stresses strongly reduce the effective tangent stiffness; beyond this region, geometric nonlinearity contributes to a partial stiffness recovery. Furthermore, the material length-scale parameter significantly enhances stiffness at small scales, increasing the frequency by up to 20% in the low-temperature regime, while its influence diminishes near the frequency-minimum temperature. The applied magnetic potential exhibits a stabilizing effect, increasing the frequency by approximately 10–25%, whereas the electric potential induces a softening behavior and shifts the frequency-minimum temperature to lower values, accelerating instability. In addition, the incorporation of an elastic foundation is shown to significantly improve structural stability, with increasing foundation stiffness suppressing thermal softening and delaying the onset of instability. Overall, the study demonstrates that the nonlinear vibration behavior of auxetic-core MEE sandwich plates is governed by a strong competition between thermal softening and multi-field-induced stiffness modulation. The findings provide new physical insight and practical guidelines for the design of advanced smart structures operating under severe multi-field environments.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5021 - 5054"},"PeriodicalIF":4.0,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00707-026-04763-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vibration analysis of AFG nanobeams with elastic boundary constraints carrying a concentrated mass at an arbitrary position based on the stress-driven nonlocal integral model with discontinuity","authors":"Shuwen Cao,&nbsp;Pei Zhang,&nbsp;Peter Schiavone","doi":"10.1007/s00707-026-04776-5","DOIUrl":"10.1007/s00707-026-04776-5","url":null,"abstract":"<div><p>We present a study on the size-dependent free vibration and frequency shifts of axially functionally graded (AFG) nanobeams functioning as resonant mass sensors. The nanobeam resonators are subject to general elastic boundary constraints, and the influence of axial-lateral vibration coupling induced by an attached concentrated mass is taken into account. Unlike traditional analyses that rely on the mathematically ill-posed strain-driven nonlocal theory, the present work adopts the well-posed stress-driven nonlocal integral elasticity model for effectively capturing the size-dependent mechanical behavior (stiffness-hardening effect), while eliminating the inherent conflict between the constitutive relation and structural equilibrium. Owing to the domain discontinuity introduced by the attached mass, both the standard and constitutive matching conditions at the mass attachment point are established. The generalized differential quadrature method (GDQM) is subsequently employed to discretize the differential problem governing the dimensionless equations of motion and the associated boundary/continuity constraints. After validating the proposed modeling framework against available literature for simplified cases, extensive parametric investigations are conducted. The combined effects of the nonlocal parameter, AFG index, magnitude and position of the concentrated mass, and the stiffness of the elastic boundary constraints on the resonant frequencies and sensor sensitivity (frequency shift ratios) are thoroughly explored. The results offer rigorous theoretical guidance for evaluating and optimizing advanced AFG micro/nanomechanical mass-sensing devices.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5105 - 5128"},"PeriodicalIF":4.0,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Galerkin weak formulation of micropolar elasticity theory for analyzing the 3D static bending and free vibration characteristics of homogeneous and functionally graded micropolar plates","authors":"Chih-Ping Wu,&nbsp;Chen-Chieh Huang,&nbsp;Ting-Yu Chang","doi":"10.1007/s00707-026-04754-x","DOIUrl":"10.1007/s00707-026-04754-x","url":null,"abstract":"<div><p>Applying Hamilton’s principle, we derive a Galerkin weak formulation of micropolar elasticity theory (MPET). Subsequently, based on this formulation, we further develop a size-dependent finite layer method (FLM) to investigate the static bending and free vibration characteristics of a simply supported, functionally graded (FG) micropolar plate. In the formulation, the micropolar plate is artificially divided into <i>n</i>_<i>l</i> layers, with equal or unequal thicknesses. Six degrees of freedom, including three displacements and three microrotations, are selected to be the primary variables for each nodal surface. MPET’s applicability to aluminum (Al), epoxy (Ep), syntactic foam (SyF), and polyurethane foam (PUF) micropolar plates is examined, revealing that microrotation effects are significant for SyF and PUF micropolar plates and nearly no impact for Al and Ep ones. After validating the MPET-based size-dependent FLM against relevant exact solutions reported in the literature, we conduct a parametric study of FG SyF and PUF micropolar plates to assess the influence of key factors on their static bending and free vibration characteristics. These factors include the inhomogeneity index, length-to-thickness ratio, aspect ratio, and microrotation, which are identified as significant. The results for different Lagrange polynomial orders of modal displacements and microrotations are compared and discussed. Considering accuracy and computational efficiency, we recommend the optimal orders for in-plane displacement (<i>n</i>₁), out-of-plane displacement (<i>n</i>₂), in-plane microrotations (<i>n</i>₃), and out-of-plane microrotation (<i>n</i>₄) are <i>n</i>₁ = 3, <i>n</i>₂ = 2, <i>n</i>₃ = 2, <i>n</i>₄ = 3.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"4993 - 5019"},"PeriodicalIF":4.0,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00707-026-04754-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Size-dependent thermoelastic vibration of nanobeams under localized heating: a hybrid analytical–ANN approach","authors":"Pham Van Vinh","doi":"10.1007/s00707-026-04759-6","DOIUrl":"10.1007/s00707-026-04759-6","url":null,"abstract":"<div><p>This study develops an efficient modeling framework to predict the size-dependent thermoelastic vibration behavior of nanobeams subjected to partially localized thermal loading and supported by Pasternak elastic foundations. The governing equations are formulated within a nonlocal elasticity framework to account for nanoscale interactions under prescribed thermomechanical fields. The expressions for natural frequencies are derived for various heating patterns, including uniform, linear, nonlinear, and sinusoidal temperature distributions with different heated length ratios. The semi-analytical solutions are validated through comparisons with available benchmark results, demonstrating excellent accuracy and reliability with a maximum relative error of only 0.0013%. Comprehensive parametric investigations elucidate the coupled influences of nonlocal effects, thermal softening, and foundation stiffness on the vibration characteristics. In addition, a feed-forward artificial neural network trained on the semi-analytical dataset is employed as a surrogate model to enable rapid and accurate frequency prediction across an extended parametric space. A key scientific contribution of this study lies in the consistent formulation of the thermally induced axial force based on equilibrium and axial strain compatibility conditions. The present methodology ensures mechanical consistency and can be readily extended to more complex structural configurations, including multi-directional functionally graded materials, non-uniform geometries, and nonlinear temperature distributions.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"4937 - 4964"},"PeriodicalIF":4.0,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-variable two-dimensional formulation using element-free basis functions for a new class of constitutive relations","authors":"Gaurav Chandra Bridhani,&nbsp;U. Saravanan","doi":"10.1007/s00707-026-04746-x","DOIUrl":"10.1007/s00707-026-04746-x","url":null,"abstract":"<div><p>This article presents a numerical formulation using element-free basis functions to solve two-dimensional boundary value problems for constitutive models in which the linearized strain and stress are implicitly related. The formulation treats both the stress and displacement fields as primary unknowns. The stress field is computed from Airy’s function, thereby satisfying equilibrium equations, and needs to be <span>({mathcal {C}}^{2})</span> continuous to satisfy the traction continuity requirement. Since developing a higher-continuity basis function for an arbitrary-shaped quadrilateral element using mesh-based interpolation techniques is infeasible, element-free basis functions are used. The Airy’s function is assumed using a linear combination of Hermite-type Moving Least Squares approximation involving a complete fifth-degree polynomial function and a new fifth-degree spline weighting function. The displacement field is assumed to be a linear combination of Moving Least Squares approximation. The unknown nodal coefficients in the assumed linear combination of stress and displacement fields are computed such that the Frobenius norm of the constitutive relation is minimized, subject to the satisfaction of constraints arising from boundary conditions. The minimized value of the Frobenius norm of the constitutive relation reflects the accuracy of the solution. The viability, efficacy, and accuracy of the proposed numerical formulation are benchmarked using six boundary value problems for two constitutive relations: linear and non-linear elastic.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"4895 - 4935"},"PeriodicalIF":4.0,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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-memory nonlocal thermoviscoelastic modeling of microcircular ceramic rings under ramp-type heating","authors":"Nikita Karde,&nbsp;Gulshan Makkad,&nbsp;Ahmed E. Abouelregal,&nbsp;Vinod Varghese","doi":"10.1007/s00707-026-04760-z","DOIUrl":"10.1007/s00707-026-04760-z","url":null,"abstract":"<div><p>This study proposes a unified dual-memory nonlocal thermoviscoelastic model for microcircular ceramic rings under ramp-type heating. The novelty lies in coupling Eringen’s nonlocal elasticity with fractional viscoelastic damping and memory-dependent thermal kernels, enabling realistic nanoscale thermomechanical analysis. The governing equations are formulated in the Laplace domain, solved analytically with modified Bessel functions, and inverted numerically via a stable Riemann-sum method. Results show that longer ramp durations mitigate thermal shock, fractional viscosity enhances damping, nonlocality smooths stress distribution, and thermal memory kernels modulate displacement amplitudes. Thickness variations amplify stress and temperature rise but leave vibration amplitude nearly unchanged. Benchmarked against classical thermoelastic models, the framework reproduces finite-speed heat waves and reveals kernel-sensitive deformation effects absent in earlier approaches. These insights provide design guidance for MEMS resonators, micro-energy harvesters, and biomedical sensors requiring reliable thermomechanical performance.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"4965 - 4991"},"PeriodicalIF":4.0,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}