International Journal of Engineering Science最新文献

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Wave dynamics in the drift-flux two-phase flow model 漂通量两相流模型中的波动动力学
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-09-22 DOI: 10.1016/j.ijengsci.2025.104385
Sumanta Shagolshem , Dia Zeidan , K.V. Nagaraja
{"title":"Wave dynamics in the drift-flux two-phase flow model","authors":"Sumanta Shagolshem ,&nbsp;Dia Zeidan ,&nbsp;K.V. Nagaraja","doi":"10.1016/j.ijengsci.2025.104385","DOIUrl":"10.1016/j.ijengsci.2025.104385","url":null,"abstract":"<div><div>The present study provides a comprehensive symmetry analysis for a simplified two-phase flow model with the logarithmic equation of state. Under a one-parameter Lie group of transformations, we generate the local symmetry of the model, preserving the invariance of the system. Subsequently, we classify one-dimensional optimal subalgebras, which is a systematic framework for computing invariant solutions efficiently. With the characteristic method, we developed explicit solutions for the model utilizing the optimal subalgebras. Further, we prove that nonlocal symmetries exist for the considered model, and then some new exact solutions were developed where local symmetries cannot provide. Furthermore, the existence of the nonlinear self-adjointness property of the model is demonstrated with the construction of conservation laws. This study concludes by examining the complex hyperbolic nature, such as <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-wave, characteristic shock, and their interaction with one of the solutions derived from nonlocal symmetry, highlighting the critical wave dynamics of the model.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104385"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145117688","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}
引用次数: 0
Elastohydrodynamic instabilities in pressure-driven flow through a poroelastic channel 孔隙弹性通道中压力驱动流体的弹性水动力不稳定性
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-09-15 DOI: 10.1016/j.ijengsci.2025.104379
Ramkarn Patne
{"title":"Elastohydrodynamic instabilities in pressure-driven flow through a poroelastic channel","authors":"Ramkarn Patne","doi":"10.1016/j.ijengsci.2025.104379","DOIUrl":"10.1016/j.ijengsci.2025.104379","url":null,"abstract":"<div><div>The linear stability analysis of a pressure-driven flow through a saturated poroelastic channel sandwiched between two impermeable rigid walls is carried out in the present study. Mixture theory is employed to describe the dynamics of the interstitial fluid and elastic solid matrix. The resulting eigenvalue problem is solved using the pseudo-spectral method. Without the poroelastic solid matrix, the flow under consideration reduces to the classical plane Poiseuille flow for which the linear stability analysis predicts critical Reynolds number, <span><math><mrow><mi>R</mi><msub><mrow><mi>e</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mn>5772</mn></mrow></math></span>. However, the present study, predicts that <span><math><mrow><mi>R</mi><msub><mrow><mi>e</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math></span> could be as low as 5 for the flow under consideration owing to the deformability of the solid matrix. Further analysis reveals the existence of three new modes of instability. For low <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span>, mode I dominates the instability, while at high <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span>, mode III dominates the instability with characteristic scaling <span><math><mrow><msub><mrow><mi>Γ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>∼</mo><mn>1</mn><mo>/</mo><mi>R</mi><mi>e</mi></mrow></math></span> where <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> is a measure of the deformability of the solid matrix. The driving mechanism of the predicted instability is found to be the coupling between the fluid and solid due to the pressure perturbation. The energy exchange between the base state velocity gradient and normal velocity perturbation via the convection term in the linearised Navier–Stokes equation plays a supporting role to the pressure perturbations in introducing unstable modes.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104379"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060540","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}
引用次数: 0
Capillary force on the inner wall of the mesh atomizer influencing the size of the droplets 网状雾化器内壁毛细力对雾滴大小的影响
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-10-16 DOI: 10.1016/j.ijengsci.2025.104399
Fan Zhang, Guan-Xian Chen, Zhen-Zhen Gui, Jian-Hui Zhang, Shao-Zheng Deng, Fu-Hai Wu, Yin-He Wang
{"title":"Capillary force on the inner wall of the mesh atomizer influencing the size of the droplets","authors":"Fan Zhang,&nbsp;Guan-Xian Chen,&nbsp;Zhen-Zhen Gui,&nbsp;Jian-Hui Zhang,&nbsp;Shao-Zheng Deng,&nbsp;Fu-Hai Wu,&nbsp;Yin-He Wang","doi":"10.1016/j.ijengsci.2025.104399","DOIUrl":"10.1016/j.ijengsci.2025.104399","url":null,"abstract":"<div><div>Piezoelectric atomizer is widely used in inhalation therapy field, where the drug deposition depth depends on the size of the atomized droplet. Herein, the diameter of the droplet was regulated by changing the wettability of the inner wall of the tapered hole of atomizers. The dynamic cone angle-capillary (DCA-C) model is established, where the contact angle of the inner wall <em>θ</em> and the cone angle <em>α</em> are the two key parameters to influence of the droplet size. When <em>θ</em>&gt;<em>π</em>/2+<em>α</em>/2, the droplet size decreases; when <em>θ</em>&lt;<em>π</em>/2+<em>α</em>/2, the droplet size increases. The experiment results show that after non-wetting treatment of the metal sheet of the atomizer, the contact angle <em>θ</em>=162°, and the atomized droplet diameter is 1.246 μm, which is decreased by 83.9%; after wetting treatment, the contact angle <em>θ</em>=66°, and the atomized droplet diameter is 9.851 μm, which is increased by 27.3%. It demonstrates that the DCA-C model can better explain the mechanism of piezoelectric atomization, where the capillary force plays a crucial role in regulating droplet size.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104399"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324314","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}
引用次数: 0
Slow translation of a slightly deformed spherical fluid drop in an arbitrary unsteady viscous flow 任意非定常粘性流动中轻微变形的球形液滴的缓慢平移
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-10-16 DOI: 10.1016/j.ijengsci.2025.104401
Chennuri Dhanya , Jai Prakash , Huan J. Keh
{"title":"Slow translation of a slightly deformed spherical fluid drop in an arbitrary unsteady viscous flow","authors":"Chennuri Dhanya ,&nbsp;Jai Prakash ,&nbsp;Huan J. Keh","doi":"10.1016/j.ijengsci.2025.104401","DOIUrl":"10.1016/j.ijengsci.2025.104401","url":null,"abstract":"<div><div>The present study investigates the translational motion of a slightly deformed spherical fluid drop suspended in an arbitrary unsteady viscous fluid. The analysis is conducted under the assumption of a negligible Reynolds number, indicating a scenario where the induced stresses are slightly higher than the interfacial tension. Consequently, the drop undergoes a slight deformation but remains intact without breaking. The flow fields in both the interior and exterior of the drop are governed by the unsteady Stokes equations, which are solved asymptotically using a method of regular perturbation expansions under appropriate boundary conditions. The deviation from the spherical shape is quantified by a small parameter referred to as the deformation parameter, which is taken as the perturbation parameter. A complete general solution to the unsteady Stokes equations is employed to solve the equations governing the fluid flow. The hydrodynamic forces on the drop are then determined and expressed in terms of Faxén’s law for an arbitrary ambient flow field. The hydrodynamic problem is tackled up to the first order of the deformation parameter, disregarding higher-order terms. Closed-form expressions for the hydrodynamic drag force acting on the drop are derived for the specific scenarios of prolate and oblate spheroidal drops. The hydrodynamic forces obtained in the present study agree with the respective hydrodynamic forces experienced by prolate and oblate spheroidal drops in the limiting case of steady flow, as existing in the literature.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104401"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324313","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}
引用次数: 0
Topology optimization of 2D chiral metamaterials with dilatation-shear and shear-shear coupling capabilities 具有膨胀-剪切和剪切-剪切耦合能力的二维手性超材料拓扑优化
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-09-04 DOI: 10.1016/j.ijengsci.2025.104367
Mohamed Shaat , Xin-Lin Gao
{"title":"Topology optimization of 2D chiral metamaterials with dilatation-shear and shear-shear coupling capabilities","authors":"Mohamed Shaat ,&nbsp;Xin-Lin Gao","doi":"10.1016/j.ijengsci.2025.104367","DOIUrl":"10.1016/j.ijengsci.2025.104367","url":null,"abstract":"<div><div>Metamaterials with chiral microstructures exhibit unique mechanical coupling among various deformation modes. Traditional approaches for designing such materials rely heavily on discrete models and unit cells with predefined architectures, and hence it has been challenging to develop methodologies that can explore a broad range of chiral configurations and optimize the mechanical coupling behavior without being constrained by specific unit cell geometries. In the current study, a new multi-objective topology optimization (TO) method is developed for designing 2D chiral metamaterials with prescribed mechanical coupling among dilatation and two distinct shear deformation modes. The new method incorporates material symmetry constraints (including the <span><math><msub><mi>C</mi><mn>2</mn></msub></math></span> and <span><math><msub><mi>C</mi><mn>4</mn></msub></math></span> symmetries) into the TO process. A strain energy-based homogenization approach is adopted to determine the effective elastic stiffness matrix for each periodic chiral metamaterial. The TO process begins with maximizing the trace of the stiffness matrix to avoid cases with vanishing bulk or shear moduli, which is followed by maximizing/minimizing a selected off-diagonal component to optimize the dilatation-shear or shear-shear coupling. The proposed method successfully identifies optimal topologies that exhibit chiral layouts consistent with the imposed material symmetry constraints, and it maximizes mechanical coupling among dilatation and shear deformation modes. This newly developed method enables the exploration of diverse chiral material configurations, achieving optimized mechanical coupling without relying on a specific unit cell architecture.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104367"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996695","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}
引用次数: 0
A peridynamic approach to analysis of coupled magneto-electro-mechanical systems 磁-电-机械耦合系统的周动力学分析方法
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-09-29 DOI: 10.1016/j.ijengsci.2025.104391
Anasuyakumari Maram, Subrata Mondal, Sudarshan Dhua
{"title":"A peridynamic approach to analysis of coupled magneto-electro-mechanical systems","authors":"Anasuyakumari Maram,&nbsp;Subrata Mondal,&nbsp;Sudarshan Dhua","doi":"10.1016/j.ijengsci.2025.104391","DOIUrl":"10.1016/j.ijengsci.2025.104391","url":null,"abstract":"<div><div>A non-ordinary state-based peridynamic model(NOSBPD) is presented for linear piezoelectromagnetic material(PEM). The corresponding material model is developed by establishing the connection between the classical theory of piezoelectromagnetics and the newly proposed peridynamic framework. The variational approach and Hamiltonian principle are utilised to establish the equation of motion. This investigation shows the effectiveness of the proposed model to handle piezoelectromagnetic material. It is also shown that the considered stabilisation method effectively reduces the instabilities of NOSBPD. The dynamic behaviour of piezoelectromagnetic material in the proposed framework is investigated. The dispersion relations for stabilised versions of NOSBPD in one and two dimensions are established analytically for PEM. The graphs illustrate the influence of <span><math><mi>δ</mi></math></span> and different nonlocality functions on frequency, phase velocity, and group velocity. Also, the significant impact of critical coupling parameters on frequency is studied using graphical demonstration. Piezoelectromagnetic materials are used in a wide range of applications to constitute transducers such as actuators and sensors. Gaining insight into their wave and vibrational properties is indispensable for the advancement of reliable and optimised devices.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104391"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145182900","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}
引用次数: 0
Predictive asymptotic models of damage evolution in thin adhesives with tension–compression asymmetry 具有拉压不对称的薄胶粘剂损伤演化的预测渐近模型
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-09-18 DOI: 10.1016/j.ijengsci.2025.104384
Michele Serpilli , Raffaella Rizzoni , Frédéric Lebon
{"title":"Predictive asymptotic models of damage evolution in thin adhesives with tension–compression asymmetry","authors":"Michele Serpilli ,&nbsp;Raffaella Rizzoni ,&nbsp;Frédéric Lebon","doi":"10.1016/j.ijengsci.2025.104384","DOIUrl":"10.1016/j.ijengsci.2025.104384","url":null,"abstract":"<div><div>In structural engineering, accurate modeling of material damage is crucial, particularly the tension–compression asymmetry observed in quasi-brittle materials and adhesive joints. While cohesive interface models are commonly employed in the analysis of bonded structures, the parameters of these models frequently lack a direct correlation with the physical properties of the adhesive layer. To address this issue and capture the tension–compression asymmetry, this study uses asymptotic analysis to derive two new interface damage models (termed F1d and F2d) from a thin damaging interphase. The proposed models are formulated within a thermodynamically consistent framework. The F1d model uses a single damage variable with an asymmetric evolution law, whereas the more advanced F2d model uses separate variables for tensile and compressive damage, enabling independent evolution kinetics. To bridge the gap between scales and link macroscopic damage to micro-defect evolution, the new models are coupled with two micromechanical schemes: the non-interacting Kachanov–Sevostianov model and the Mori–Tanaka–Benveniste model, the latter of which accounts for defect interactions. The theoretical formulations of the models are presented, and their predictive capabilities are demonstrated through numerical simulations of a bonded joint under axial loading.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104384"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145095238","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}
引用次数: 0
Analytical study to control phase gradient in elastic meta-interface for wave mode conversions 波型转换弹性元界面中相位梯度控制的解析研究
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-09-23 DOI: 10.1016/j.ijengsci.2025.104388
Mohammad Daud, Jongmin Shim
{"title":"Analytical study to control phase gradient in elastic meta-interface for wave mode conversions","authors":"Mohammad Daud,&nbsp;Jongmin Shim","doi":"10.1016/j.ijengsci.2025.104388","DOIUrl":"10.1016/j.ijengsci.2025.104388","url":null,"abstract":"<div><div>We present an analytical and design framework for achieving efficient elastic wave mode conversion across meta-interfaces governed by Generalized Snell’s Law (GSL), which prescribes wave motion based on a spatial phase gradient along the interface. In contrast to conventional optimization-based approaches, our method provides clear physical insight into the mechanism of pressure-to-shear wave conversion through a simplified one-dimensional axial wave model with the transfer matrix approach. This model yields analytical expressions for geometric conditions and identifies the relevant design parameter space. Based on this framework, we propose a compact chiral-pattern subunit with a frequency-scalable geometry, enabling straightforward implementation across a range of wave conditions. Full-scale numerical simulations confirm that the resulting meta-interface achieves strong mode conversion performance and accurately reproduces key phenomena including transmitted angles. Additionally, we demonstrate symmetric transmission by introducing mirrored phase gradients, further validating the flexibility of the GSL-based design. While the conversion efficiency is constrained by angular limits inherent to the material’s Poisson ratio, the framework provides a foundation for future improvements. This work bridges analytical modeling and practical design, offering an interpretable and scalable approach to engineered wave manipulation.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104388"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145117687","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}
引用次数: 0
Tug-of-war between liquids and membranes 液体和膜之间的拔河
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-10-08 DOI: 10.1016/j.ijengsci.2025.104395
Weiting Chen, Quanzi Yuan
{"title":"Tug-of-war between liquids and membranes","authors":"Weiting Chen,&nbsp;Quanzi Yuan","doi":"10.1016/j.ijengsci.2025.104395","DOIUrl":"10.1016/j.ijengsci.2025.104395","url":null,"abstract":"<div><div>Predicting the deformation behavior of an initially stressed membrane subjected to liquid self-weight is nontrivial. Experimental observation indicates that in the tug-of-war competition between liquids and membranes, which side will prevail does not depend on the liquid volume. However, the existing models cannot explain this counterintuitive phenomenon. With the aim of understanding the underlying mechanics behind those unexpected features, we propose a theoretical model for deriving the configuration of membrane–liquid interactions. The analytical solutions for one-dimensional and two-dimensional axisymmetric membrane deflections are derived by combining the linear membrane theory and configuration-dependent loading. These solutions yield quantitative predictions for the three types of configuration that are in excellent agreement with the experiments. Remarkably, we find that a dimensionless parameter concerning the liquid density, the size of the system, and the membrane tension controls the intensity of the membrane–liquid competition. Our model opens up a new perspective for studying fluid–structure interaction systems.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104395"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145264995","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}
引用次数: 0
A novel computational framework for wave propagation analysis of periodic 3D small-size solids 周期性三维小尺寸固体波传播分析的新计算框架
IF 5.7 1区 工程技术
International Journal of Engineering Science Pub Date : 2025-12-01 Epub Date: 2025-07-28 DOI: 10.1016/j.ijengsci.2025.104350
Andrea Francesco Russillo, Giuseppe Failla
{"title":"A novel computational framework for wave propagation analysis of periodic 3D small-size solids","authors":"Andrea Francesco Russillo,&nbsp;Giuseppe Failla","doi":"10.1016/j.ijengsci.2025.104350","DOIUrl":"10.1016/j.ijengsci.2025.104350","url":null,"abstract":"<div><div>Analysing elastic wave propagation in periodic small-size structures plays an important role in the design of many micro- and nano-engineering devices. However, as ad hoc size-dependent continuum theories are required to capture size effects, pertinent computational tools shall be developed to characterize the wave propagation properties. In this context, this paper introduces an original computational framework to build the dispersion diagram of periodic 3D small-size solids of arbitrary shape, as modelled by the well-established Eringen’s nonlocal integral theory. The framework makes use of a suitable periodic Bloch ansatz to represent the response variables involved in the weak formulation of the integro-differential free-vibration equilibrium equations of the unit cell. Building on the periodicity of the Bloch ansatz and introducing an appropriate change of variables, it is shown that the integral coupling the response at a given point of the unit cell to the responses at all points of the solid can be reverted to the summation of integrals defined on the domain of the unit cell only. This remarkable result paves the way to solve the wave propagation problem by a finite element formulation of the free-vibration equilibrium equations of the unit cell, which involves a standard mass matrix, a local stiffness matrix and a nonlocal stiffness matrix, with the latter being expressed by the infinite summation of nonlocal matrices accounting for the nonlocal interactions between the unit cell and the surrounding cells of the solid. In fact, the summation can be truncated to a finite order depending on the nonlocal horizon of the kernel function selected for the nonlocal integral model and the dispersion diagram can be obtained from a linear eigenvalue problem, derived enforcing the Bloch conditions in the finite element free-vibration equilibrium equations of the unit cell. Numerical applications substantiate correctness and accuracy of the proposed framework, which enables a consistent application of the Eringen’s nonlocal integral theory to study wave propagation in periodic 3D small-size structures of arbitrary shape, for the first time to the best of authors’ knowledge.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104350"},"PeriodicalIF":5.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713665","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}
引用次数: 0
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