Pub Date : 2025-10-01DOI: 10.1016/j.mechrescom.2025.104539
Sudip Chowdhury, Sondipon Adhikari
Structural vibration control is essential for enhancing the safety and longevity of engineering systems. Traditional Tuned Mass Dampers (TMDs) effectively mitigate vibrations but are limited by their reliance on large auxiliary masses. To address this challenge, we propose the Frictional Energy Harvesting Vibration Absorber (FEHVA), a novel hybrid absorber that integrates frictional damping with energy harvesting. The governing equations of FEHVA are derived using the statistical linearisation method, and optimal design parameters are determined via H optimisation. Dynamic response evaluations reveal that FEHVA achieves up to 14.20% improved vibration reduction over conventional TMDs under harmonic and random excitations. Furthermore, comparisons with the Inerter Energy Harvesting Vibration Absorber (IEHVA) show that FEHVA provides 85.97% superior vibration attenuation, demonstrating its efficiency in broadband vibration mitigation. The hybrid combination of frictional damping and energy harvesting significantly enhances structural resilience while generating electrical power. These results establish FEHVA as a robust, sustainable alternative for vibration control in civil engineering applications. By offering enhanced damping and energy harvesting simultaneously, FEHVA presents a step forward in the development of multifunctional vibration absorbers, advancing future engineering solutions for infrastructure subjected to dynamic loads.
{"title":"Frictional Energy Harvesting Vibration Absorbers","authors":"Sudip Chowdhury, Sondipon Adhikari","doi":"10.1016/j.mechrescom.2025.104539","DOIUrl":"10.1016/j.mechrescom.2025.104539","url":null,"abstract":"<div><div>Structural vibration control is essential for enhancing the safety and longevity of engineering systems. Traditional Tuned Mass Dampers (TMDs) effectively mitigate vibrations but are limited by their reliance on large auxiliary masses. To address this challenge, we propose the Frictional Energy Harvesting Vibration Absorber (FEHVA), a novel hybrid absorber that integrates frictional damping with energy harvesting. The governing equations of FEHVA are derived using the statistical linearisation method, and optimal design parameters are determined via H<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> optimisation. Dynamic response evaluations reveal that FEHVA achieves up to 14.20% improved vibration reduction over conventional TMDs under harmonic and random excitations. Furthermore, comparisons with the Inerter Energy Harvesting Vibration Absorber (IEHVA) show that FEHVA provides 85.97% superior vibration attenuation, demonstrating its efficiency in broadband vibration mitigation. The hybrid combination of frictional damping and energy harvesting significantly enhances structural resilience while generating electrical power. These results establish FEHVA as a robust, sustainable alternative for vibration control in civil engineering applications. By offering enhanced damping and energy harvesting simultaneously, FEHVA presents a step forward in the development of multifunctional vibration absorbers, advancing future engineering solutions for infrastructure subjected to dynamic loads.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104539"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/j.mechrescom.2025.104536
A. Cruzado, A.A. Benzerga
Void growth and coalescence are investigated in a class of non-uniform void populations under load conditions of overall axial symmetry. Fast Fourier transform based finite strain calculations were carried out using three-dimensional periodic cells containing monodispersed equiaxed voids embedded in an elastic–plastic matrix with isotropic linear hardening. Constant stress triaxiality was maintained in a given calculation and a range of triaxialities were explored. Both the overall stress–strain relation of the porous material and the evolution of porosity are natural outcomes to this type of analysis. In particular, circumstances were examined under which a transition to uniaxial straining of the cell occurs, thereby introducing a measure of ductility. The results show that nonuniform void dispersions do not necessarily lower the overall ductility relative to a reference ordered (simple cubic) dispersion. This finding is interpreted in light of the inherent competition between a recently uncovered phenomenon of distribution softening and persistent isotropy in void spacing evolution.
{"title":"Analysis of void coalescence accounting for nonuniform void distributions","authors":"A. Cruzado, A.A. Benzerga","doi":"10.1016/j.mechrescom.2025.104536","DOIUrl":"10.1016/j.mechrescom.2025.104536","url":null,"abstract":"<div><div>Void growth and coalescence are investigated in a class of non-uniform void populations under load conditions of overall axial symmetry. Fast Fourier transform based finite strain calculations were carried out using three-dimensional periodic cells containing monodispersed equiaxed voids embedded in an elastic–plastic matrix with isotropic linear hardening. Constant stress triaxiality was maintained in a given calculation and a range of triaxialities were explored. Both the overall stress–strain relation of the porous material and the evolution of porosity are natural outcomes to this type of analysis. In particular, circumstances were examined under which a transition to uniaxial straining of the cell occurs, thereby introducing a measure of ductility. The results show that nonuniform void dispersions do not necessarily lower the overall ductility relative to a reference ordered (simple cubic) dispersion. This finding is interpreted in light of the inherent competition between a recently uncovered phenomenon of distribution softening and persistent isotropy in void spacing evolution.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104536"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/j.mechrescom.2025.104543
You-Chuan Chou , Falin Chen , Min-Hsing Chang
This study investigates the stability of a rotating horizontal nanofluid layer confined between two rigid plates and uniformly heated from below. The mechanism of gravitational settling of nanoparticles is incorporated into the convective transport model to describe the relative slip motion of nanoparticles within the base fluid in addition to the effects of thermophoresis and Brownian motion. Aqueous aluminum oxide nanofluids with three representative nanoparticle diameters: 20, 40, and 60 nm, are examined to evaluate the influence of gravitational settling on instability behavior. A linear stability analysis is performed and the results reveal that rotation acts as a stabilizing mechanism. However, this stabilizing effect diminishes gradually with increasing nanoparticle volume fraction. Enhanced gravitational settling effect promotes the flow stability significantly, and its interplay with thermophoresis induces the onset of oscillatory mode at low Taylor number (Ta) condition. As Ta increases, the oscillatory mode is progressively suppressed and the onset of instability is eventually governed by the stationary mode with a higher critical wavenumber. Particularly, once the size of nanoparticles is large enough, a bimodal neutral curve is observed and the critical mode may shift from stationary to oscillatory mode with increasing the volume fraction of nanoparticles. These findings demonstrate that the instability characteristics in a rotating nanofluid layer deviate significantly from those observed in a classical rotating fluid layer, and reveal the pivotal role of gravitational settling in the nature and threshold of thermally driven instability in this flow system.
{"title":"Gravitational settling effect of nanoparticles on the onset of thermal convection in a rotating nanofluid layer","authors":"You-Chuan Chou , Falin Chen , Min-Hsing Chang","doi":"10.1016/j.mechrescom.2025.104543","DOIUrl":"10.1016/j.mechrescom.2025.104543","url":null,"abstract":"<div><div>This study investigates the stability of a rotating horizontal nanofluid layer confined between two rigid plates and uniformly heated from below. The mechanism of gravitational settling of nanoparticles is incorporated into the convective transport model to describe the relative slip motion of nanoparticles within the base fluid in addition to the effects of thermophoresis and Brownian motion. Aqueous aluminum oxide nanofluids with three representative nanoparticle diameters: 20, 40, and 60 nm, are examined to evaluate the influence of gravitational settling on instability behavior. A linear stability analysis is performed and the results reveal that rotation acts as a stabilizing mechanism. However, this stabilizing effect diminishes gradually with increasing nanoparticle volume fraction. Enhanced gravitational settling effect promotes the flow stability significantly, and its interplay with thermophoresis induces the onset of oscillatory mode at low Taylor number (<em>Ta</em>) condition. As <em>Ta</em> increases, the oscillatory mode is progressively suppressed and the onset of instability is eventually governed by the stationary mode with a higher critical wavenumber. Particularly, once the size of nanoparticles is large enough, a bimodal neutral curve is observed and the critical mode may shift from stationary to oscillatory mode with increasing the volume fraction of nanoparticles. These findings demonstrate that the instability characteristics in a rotating nanofluid layer deviate significantly from those observed in a classical rotating fluid layer, and reveal the pivotal role of gravitational settling in the nature and threshold of thermally driven instability in this flow system.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104543"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/j.mechrescom.2025.104535
I. Argatov , A. Papangelo
A fibrillar interface is modeled as a regular array of cylindrical micropillars bonded to a substrate, with a focus on the viscoelastic properties of the fibrils. A one-dimensional linear constitutive model describes the coupled deformation of an individual fibril and the substrate. For a compliant viscoelastic substrate, the interaction backing layer effect between fibrils through the substrate deformations is also accounted for. In the case of a viscoelastic Winkler-type foundation whose adhesive mechanism is described by the Shrimali–Lopez-Pamies criterion of maximum rate-independent elongation of the foundation elements, an exact analytical solution is derived for the displacement-controlled loading protocol. A leading-order discrete asymptotic model is developed for the Schapery-type rate-independent adhesive contact between the viscoelastic fibrillar substrate and a rigid punch. By neglecting the influence of the backing layer, a homogenized model is derived in detail. The debonding incubation time is introduced, and an analytical approximation for the pull-off force is obtained under conditions of strong adhesion and fast unloading after a long dwell time.
{"title":"Adhesive contact of a viscoelastic fibrillar surface — A homogenized model","authors":"I. Argatov , A. Papangelo","doi":"10.1016/j.mechrescom.2025.104535","DOIUrl":"10.1016/j.mechrescom.2025.104535","url":null,"abstract":"<div><div>A fibrillar interface is modeled as a regular array of cylindrical micropillars bonded to a substrate, with a focus on the viscoelastic properties of the fibrils. A one-dimensional linear constitutive model describes the coupled deformation of an individual fibril and the substrate. For a compliant viscoelastic substrate, the interaction backing layer effect between fibrils through the substrate deformations is also accounted for. In the case of a viscoelastic Winkler-type foundation whose adhesive mechanism is described by the Shrimali–Lopez-Pamies criterion of maximum rate-independent elongation of the foundation elements, an exact analytical solution is derived for the displacement-controlled loading protocol. A leading-order discrete asymptotic model is developed for the Schapery-type rate-independent adhesive contact between the viscoelastic fibrillar substrate and a rigid punch. By neglecting the influence of the backing layer, a homogenized model is derived in detail. The debonding incubation time is introduced, and an analytical approximation for the pull-off force is obtained under conditions of strong adhesion and fast unloading after a long dwell time.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104535"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/j.mechrescom.2025.104537
Dilek Demirkuş
The aim of this paper is, analytically and numerically, to deal with the nonlinear modulation of Love waves in a single-layered half-space. In this study, the propagation of Love waves in a solid half-space covered by a solid layer is considered. Both mediums contain nonlinear, isotopic, hyper-elastic, and generalized neo-Hookean materials. Additionally, the layer consists of homogeneous materials and the half-space involves heterogeneous materials. Heterogeneity varies with the thickness and is uniform in any direction parallel to the boundaries. Furthermore, the upper surface to be free from traction, and displacements and stresses to be continuous at the interface are assumed, in addition to holding the radiation condition in the half-space. It is noted that this problem corresponds to the improved version of Love wave propagation. An improvement is from linearity to nonlinearity and from homogeneity to heterogeneity. Therefore, the improved version of Love wave dispersion is obtained and the nonlinear modulation of Love waves is given by the nonlinear Schrödinger equation. Moreover, the existence of bright and dark solitary Love wave solutions, as a result of balancing between dispersion and nonlinearity, is investigated. In this context, the effects of parameters of linear and nonlinear mediums are, graphically, given in details.
{"title":"Propagation of Love waves in a homogeneous layer overlying a heterogeneous half-space","authors":"Dilek Demirkuş","doi":"10.1016/j.mechrescom.2025.104537","DOIUrl":"10.1016/j.mechrescom.2025.104537","url":null,"abstract":"<div><div>The aim of this paper is, analytically and numerically, to deal with the nonlinear modulation of Love waves in a single-layered half-space. In this study, the propagation of Love waves in a solid half-space covered by a solid layer is considered. Both mediums contain nonlinear, isotopic, hyper-elastic, and generalized neo-Hookean materials. Additionally, the layer consists of homogeneous materials and the half-space involves heterogeneous materials. Heterogeneity varies with the thickness and is uniform in any direction parallel to the boundaries. Furthermore, the upper surface to be free from traction, and displacements and stresses to be continuous at the interface are assumed, in addition to holding the radiation condition in the half-space. It is noted that this problem corresponds to the improved version of Love wave propagation. An improvement is from linearity to nonlinearity and from homogeneity to heterogeneity. Therefore, the improved version of Love wave dispersion is obtained and the nonlinear modulation of Love waves is given by the nonlinear Schrödinger equation. Moreover, the existence of bright and dark solitary Love wave solutions, as a result of balancing between dispersion and nonlinearity, is investigated. In this context, the effects of parameters of linear and nonlinear mediums are, graphically, given in details.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104537"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/j.mechrescom.2025.104528
C. Balitactac, C. Rodriguez
Many viscous liquids behave effectively as incompressible under high pressures but display a pronounced dependence of viscosity on pressure. The classical incompressible Navier–Stokes model cannot account for both features, and a simple pressure-dependent modification introduces questions about the well-posedness of the resulting equations. This paper presents the first study of a second-gradient extension of the incompressible Navier–Stokes model, recently introduced by the authors, which includes higher-order spatial derivatives, pressure-sensitive viscosities, and complementary boundary conditions. Focusing on steady flow down an inclined plane, we adopt Barus’ exponential law and impose weak adherence at the lower boundary and a prescribed ambient pressure at the free surface. Through numerical simulations, we examine how the flow profile varies with the angle of inclination, ambient pressure, viscosity sensitivity to pressure, and internal length scale.
{"title":"Inclined flow of a second-gradient incompressible fluid with pressure-dependent viscosity","authors":"C. Balitactac, C. Rodriguez","doi":"10.1016/j.mechrescom.2025.104528","DOIUrl":"10.1016/j.mechrescom.2025.104528","url":null,"abstract":"<div><div>Many viscous liquids behave effectively as incompressible under high pressures but display a pronounced dependence of viscosity on pressure. The classical incompressible Navier–Stokes model cannot account for both features, and a simple pressure-dependent modification introduces questions about the well-posedness of the resulting equations. This paper presents the first study of a second-gradient extension of the incompressible Navier–Stokes model, recently introduced by the authors, which includes higher-order spatial derivatives, pressure-sensitive viscosities, and complementary boundary conditions. Focusing on steady flow down an inclined plane, we adopt Barus’ exponential law and impose weak adherence at the lower boundary and a prescribed ambient pressure at the free surface. Through numerical simulations, we examine how the flow profile varies with the angle of inclination, ambient pressure, viscosity sensitivity to pressure, and internal length scale.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104528"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/j.mechrescom.2025.104532
N. Valdivia , P.M. Jordan
Employing a combination of analytical and numerical methodologies, we investigate the propagation and evolution of acoustic acceleration waves in lossless bubbly liquids under the (1D) finite-amplitude model termed the Crighton–Westervelt–Klein–Gordon (CWKG) equation. Exact acceleration wave results for the acoustic pressure field are derived and analyzed, and special/limiting cases are identified. It is shown that by varying the value of the parameter that represents the volume concentration of bubbles, one can control the instant at which “gradient catastrophe” (i.e., shock formation) occurs. Results obtained are also compared with those for both the bubble-free limiting case of the CWKG equation and the classic Klein–Gordon equation, which is the linearized version of the CWKG equation. Lastly, a link between the present model and an extension of the Fermi–Pasta–Ulam–Tsingou- case is noted.
采用解析和数值方法相结合的方法，我们研究了无损气泡液体中声加速度波在一维有限振幅模型下的传播和演化，称为crightton - westervelt - klein - gordon （CWKG）方程。推导和分析了声压场的精确加速度波结果，并识别了特殊/极限情况。结果表明，通过改变代表气泡体积浓度的参数值，可以控制“梯度突变”（即激波形成）发生的瞬间。并将所得结果与CWKG方程无气泡极限情况和经典Klein-Gordon方程（CWKG方程的线性化版本）的结果进行了比较。最后，指出了当前模型与Fermi-Pasta-Ulam-Tsingou -α案例的扩展之间的联系。
{"title":"Transient phenomena under the Crighton–Westervelt–Klein–Gordon equation: Controlling the onset of gradient catastrophe in bubbly liquids","authors":"N. Valdivia , P.M. Jordan","doi":"10.1016/j.mechrescom.2025.104532","DOIUrl":"10.1016/j.mechrescom.2025.104532","url":null,"abstract":"<div><div>Employing a combination of analytical and numerical methodologies, we investigate the propagation and evolution of acoustic acceleration waves in lossless bubbly liquids under the (1D) finite-amplitude model termed the Crighton–Westervelt–Klein–Gordon (CWKG) equation. Exact acceleration wave results for the acoustic pressure field are derived and analyzed, and special/limiting cases are identified. It is shown that by varying the value of the parameter that represents the volume concentration of bubbles, one can control the instant at which “gradient catastrophe” (i.e., shock formation) occurs. Results obtained are also compared with those for both the bubble-free limiting case of the CWKG equation and the classic Klein–Gordon equation, which is the linearized version of the CWKG equation. Lastly, a link between the present model and an extension of the Fermi–Pasta–Ulam–Tsingou-<span><math><mi>α</mi></math></span> case is noted.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104532"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/j.mechrescom.2025.104531
Alexander V. Lopatin , Alexander V. Tololo , Sergey A. Pikulin
In the paper an analytical solution to the problem of determining the fundamental frequency of vibrations of a rectangular orthotropic plate with uniformly distributed point supports is obtained. The deflection and the two rotation angles of the tangents are equal to zero at each point of support of the plate. The edges of the plate are fully clamped. The solution to the required dynamic problem is reduced to the determination of the fundamental frequency of vibrations of a rectangular fragment of a plate supported at four corner points. At each of the edges of such a plate fragment, the angle of rotation of the tangent and the generalised shear force are both zero. The solution to the dynamic problem for the plate fragment was obtained by employing the Ritz method. An approximation of the deflection of a plate fragment supported at four corners was performed using a three-term combination of clamped–clamped beam functions. The implementation of the Ritz method enabled the derivation of a cubic equation, from which the desired frequency of vibration of the corned supported plate fragment was subsequently ascertained by the Cardano method. The analytical solution was utilised to calculate the fundamental frequency of vibrations of the orthotropic plate fragment with given sizes. The found frequency was then compared with the fundamental frequency of vibrations of whole plates with uniformly distributed point supports. The calculation of the latter was performed by means of the finite element method. The comparison demonstrated that the fundamental frequency of vibrations of whole plates slightly exceeds the frequency of vibrations of their fragments. It is evident that the discrepancy between these frequencies diminishes as the number of fragments along the edges of the plates increases. The paper demonstrates the use of the value of the fundamental frequency of fragment vibrations in the design of point-supported plates.
{"title":"Fundamental frequency of an orthotropic rectangular plate with uniformly distributed point supports: Application to the design procedure","authors":"Alexander V. Lopatin , Alexander V. Tololo , Sergey A. Pikulin","doi":"10.1016/j.mechrescom.2025.104531","DOIUrl":"10.1016/j.mechrescom.2025.104531","url":null,"abstract":"<div><div>In the paper an analytical solution to the problem of determining the fundamental frequency of vibrations of a rectangular orthotropic plate with uniformly distributed point supports is obtained. The deflection and the two rotation angles of the tangents are equal to zero at each point of support of the plate. The edges of the plate are fully clamped. The solution to the required dynamic problem is reduced to the determination of the fundamental frequency of vibrations of a rectangular fragment of a plate supported at four corner points. At each of the edges of such a plate fragment, the angle of rotation of the tangent and the generalised shear force are both zero. The solution to the dynamic problem for the plate fragment was obtained by employing the Ritz method. An approximation of the deflection of a plate fragment supported at four corners was performed using a three-term combination of clamped–clamped beam functions. The implementation of the Ritz method enabled the derivation of a cubic equation, from which the desired frequency of vibration of the corned supported plate fragment was subsequently ascertained by the Cardano method. The analytical solution was utilised to calculate the fundamental frequency of vibrations of the orthotropic plate fragment with given sizes. The found frequency was then compared with the fundamental frequency of vibrations of whole plates with uniformly distributed point supports. The calculation of the latter was performed by means of the finite element method. The comparison demonstrated that the fundamental frequency of vibrations of whole plates slightly exceeds the frequency of vibrations of their fragments. It is evident that the discrepancy between these frequencies diminishes as the number of fragments along the edges of the plates increases. The paper demonstrates the use of the value of the fundamental frequency of fragment vibrations in the design of point-supported plates.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104531"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/j.mechrescom.2025.104547
S.C.F. Fernandes , J. Cuartero , A.J.M. Ferreira
Using the Reddy higher-order shell theory, a highly effective pseudospectral solution for the free vibration analysis of laminated shells is presented, using Kronecker products to gather the differentiation matrices for two-dimensional problems and Chebyshev polynomials to generate univariate differentiation matrices.
{"title":"Free vibration analysis of doubly-curved laminated shells by pseudospectrals and Reddy’s higher-order shell theory","authors":"S.C.F. Fernandes , J. Cuartero , A.J.M. Ferreira","doi":"10.1016/j.mechrescom.2025.104547","DOIUrl":"10.1016/j.mechrescom.2025.104547","url":null,"abstract":"<div><div>Using the Reddy higher-order shell theory, a highly effective pseudospectral solution for the free vibration analysis of laminated shells is presented, using Kronecker products to gather the differentiation matrices for two-dimensional problems and Chebyshev polynomials to generate univariate differentiation matrices.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104547"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper addresses the question of determining local stress fields using the numerically efficient Fast Fourier Transform (FFT) method as an application of the continuum defect theory in the presence of interfacial defects, and specifically High Angle Grain Boundaries (HAGBs). First, the Field Dislocation and Disclination Mechanics (FDDM) equations are reported highlighting the use of the Stokes-Helmholtz orthogonal decomposition for both elastic strain and curvature tensors which are involved for disclination-type defects. Then, following this decomposition, both incompatible and compatible fields can be solved. Second, the Green’s function method for heterogeneous media is used to derive the stress polarization field, which integrates both dislocation and disclination densities. The compatible elastic strain tensor is numerically solved with the spectral method using the FFT (fast Fourier transform) algorithm together with finite difference (FD) schemes for computing first- and second-order spatial derivatives (FDDM-FFT). As applications of the method, the stress fields of two specific HAGBs (symmetric tilt GBs with [001] tilt axis), precisely and are obtained from the Disclination Structural Unit Model (DSUM). They are calculated assuming both isotropic and anisotropic elasticity with the present FDDM-FFT numerical method and assuming periodic disclination density tensors. Quantitative comparisons are first performed for both HAGBs with analytical solutions obtained from specific combinations of disclination dipole walls in linear isotropic elasticity. Then, the effect of anisotropic elasticity is analyzed for both HAGBS considering two different FCC metals, namely Al and Ag. Lastly, some comparisons between the FDDM-FFT-based results with molecular statics (MS) simulations, using the virial stress method and an interpolation method based on Gaussian kernel are reported for both HAGBs applied to Al and Ag. It is shown that, despite their relative simplicity in describing HAGB defect cores, the FDDM-FFT results reproduce the major trends of MS-based results for both hydrostatic and shear stress components.
{"title":"FFT-based disclination mechanics for high angle grain boundaries and comparisons with atomistic simulations","authors":"Abdallah Wazne, Joé Petrazoller, Julien Guénolé, Thiebaud Richeton, Stéphane Berbenni","doi":"10.1016/j.mechrescom.2025.104529","DOIUrl":"10.1016/j.mechrescom.2025.104529","url":null,"abstract":"<div><div>The paper addresses the question of determining local stress fields using the numerically efficient Fast Fourier Transform (FFT) method as an application of the continuum defect theory in the presence of interfacial defects, and specifically High Angle Grain Boundaries (HAGBs). First, the Field Dislocation and Disclination Mechanics (FDDM) equations are reported highlighting the use of the Stokes-Helmholtz orthogonal decomposition for both elastic strain and curvature tensors which are involved for disclination-type defects. Then, following this decomposition, both incompatible and compatible fields can be solved. Second, the Green’s function method for heterogeneous media is used to derive the stress polarization field, which integrates both dislocation and disclination densities. The compatible elastic strain tensor is numerically solved with the spectral method using the FFT (fast Fourier transform) algorithm together with finite difference (FD) schemes for computing first- and second-order spatial derivatives (FDDM-FFT). As applications of the method, the stress fields of two specific HAGBs (symmetric tilt GBs with [001] tilt axis), precisely <span><math><mrow><mi>Σ</mi><mn>29</mn><mrow><mo>(</mo><mn>520</mn><mo>)</mo></mrow><mrow><mo>[</mo><mn>001</mn><mo>]</mo></mrow><mn>46</mn><mo>.</mo><mn>40</mn><mo>°</mo></mrow></math></span> and <span><math><mrow><mi>Σ</mi><mn>149</mn><mrow><mo>(</mo><mn>1070</mn><mo>)</mo></mrow><mrow><mo>[</mo><mn>001</mn><mo>]</mo></mrow><mn>20</mn><mo>.</mo><mn>02</mn><mo>°</mo></mrow></math></span> are obtained from the Disclination Structural Unit Model (DSUM). They are calculated assuming both isotropic and anisotropic elasticity with the present FDDM-FFT numerical method and assuming periodic disclination density tensors. Quantitative comparisons are first performed for both HAGBs with analytical solutions obtained from specific combinations of disclination dipole walls in linear isotropic elasticity. Then, the effect of anisotropic elasticity is analyzed for both HAGBS considering two different FCC metals, namely Al and Ag. Lastly, some comparisons between the FDDM-FFT-based results with molecular statics (MS) simulations, using the virial stress method and an interpolation method based on Gaussian kernel are reported for both HAGBs applied to Al and Ag. It is shown that, despite their relative simplicity in describing HAGB defect cores, the FDDM-FFT results reproduce the major trends of MS-based results for both hydrostatic and shear stress components.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104529"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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