Acta Mechanica最新文献

{"title":"Canonical equations for generalized Chaplygin systems and Herglotz-type Noether theorems","authors":"Yi Zhang","doi":"10.1007/s00707-024-04204-6","DOIUrl":"10.1007/s00707-024-04204-6","url":null,"abstract":"<div><p>Herglotz’s principle is suitable for dealing with nonconservative phenomena. It is an extension of Hamilton’s principle. The generalized Chaplygin canonical equations are derived from Herglotz principle for nonconservative systems with nonholonomic constraints. The variational equation of Hamilton–Herglotz action for generalized Chaplygin systems is derived by using the Chetaev condition of constraints on virtual displacements. From this, two formulas of non-isochronous variation of the action are deduced. The definitions of Herglotz-type Noether symmetric transformation and quasi-symmetric transformation in phase space are given, and the criterion (i.e., generalized Noether identity) is derived by using total variational formula, and the Herglotz-type Noether-conserved quantities are given. Finally, a nonconservative nonholonomic system is investigated, the Herglotz-type generalized Chaplygin equation and generalized Noether identity are set up, and conservation laws are found by using the theorems we obtained, and the validity of the results is verified.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1061 - 1070"},"PeriodicalIF":2.3,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513375","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":"Decay rates for Timoshenko beam system with suspenders and arbitrary nonlinear localized damping","authors":"F. A. Falcão Nascimento,&nbsp;C. A. Nonato,&nbsp;A. J. A. Ramos,&nbsp;J. E. L. Oliveira","doi":"10.1007/s00707-024-04202-8","DOIUrl":"10.1007/s00707-024-04202-8","url":null,"abstract":"<div><p>In this article, we analyze a vibrating Timoshenko beam system with suspension in a one-dimensional bounded domain, under nonlinear localized internal damping mechanisms affecting all three wave equations. Specifically, we prove that damping applied to an arbitrarily small interval with positive measure, no matter how small, is effective. We also establish the existence and uniqueness of solutions using nonlinear semigroup theory and determine some rates of decay for these solutions without assuming any relationship between the coefficients. Additionally, we prove a result concerning internal observability for the conservative system to achieve the aforementioned asymptotic behavior.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"1487 - 1508"},"PeriodicalIF":2.3,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638509","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 vibration and primary resonance analysis of porous FG/Lipid sandwich bionanoplates based on nonlocal strain gradient theory","authors":"Abbas Moradi,&nbsp;Afshin Ghanbarzadeh,&nbsp;Mohammad Shishesaz,&nbsp;Hamid M. Sedighi","doi":"10.1007/s00707-024-04132-5","DOIUrl":"10.1007/s00707-024-04132-5","url":null,"abstract":"<div><p>Mechanical nanosensors embedded within biological systems offer unique opportunities to assess variations in mass, displacements, and forces resulting from subcellular and cellular processes. On the other hand, these mechanical nanosensors establish a foundation for biological measurement devices capable of detecting individual molecules, owing to their exceptional size compatibility with molecular interactions. To enhance the performance of micro-/nanoscale biosensors, various organic layers, including biostructures like RNA, specific antibodies, and DNA, as well as lipid layers, are employed to identify a range of physical, chemical, and biological entities. This study investigates the nonlinear vibrations and primary resonance of a bionanostructure utilizing the first-order shear deformation plate theory (FSDT) in conjunction with the nonlocal strain gradient theory (NSGT). The sandwich nanoplates comprise a functionally graded core (FG) integrated with lipid bilayers on its upper and lower surfaces. The boundary condition is specified as immovable and simply supported, and this nanobiostructure is embedded in a nonlinear elastic foundation. The impact of porosity on both free and forced vibrations of functionally graded (FG) lipid sandwich nanoplates has been examined. The viscoelastic characteristics of the lipid layers were analyzed using the Kelvin–Voigt model. The Hamiltonian principle is utilized to formulate the nonlinear differential equations governing FG/Lipid sandwich nanoplates. The resulting partial differential equations are discretized through the application of the Galerkin method. Then perturbation techniques, including the multiple scale method and the Krylov–Bogoliubov–Mitropolski approach, are employed to analytically solve the system’s equations. A good agreement has been established by juxtaposing the present numerical outcomes with the results of earlier studies. The effects of several parameters, such as nonlocal and strain gradient indices, various foundation types, porosity volume fraction, excitation force magnitudes, different plate theories, and lipid viscoelastic properties, have been comprehensively examined. Drawing from the investigations and analyses conducted in this study, the findings on the nonlinear vibration characteristics of FG/Lipid sandwich nanoplates can be applied by researchers in the development of highly biocompatible nanobiosensors, nanodevices, and resonators.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1029 - 1059"},"PeriodicalIF":2.3,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513221","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":"Geometry and pressure effects on shallow microchannel deformations","authors":"Pablo Mardones Muñoz,&nbsp;Maria Luisa Cordero","doi":"10.1007/s00707-024-04145-0","DOIUrl":"10.1007/s00707-024-04145-0","url":null,"abstract":"<div><p>Understanding the deformation of microchannels is critical for designing microfluidic devices made of soft materials and operating under significant pressure gradients. This study aims to establish an analytic elastic model for the deformation of a shallow microchannel under the action of inner pressure that includes the geometrical parameters of the whole device. By considering a rectangular prism-shaped polymeric block with a straight channel on a rigid substrate, the stress, strain, and deformation of the channel’s roof are analyzed in a plane deformation framework. The outcomes illustrate that deformation is influenced by elastic and geometric variables. This model allows qualitative and quantitative predictions of the deflection in the roof of a microchannel. The model is tested experimentally with a flowing train of droplets, finding a good quantitative agreement. However, qualitative differences might suggest a non-negligible effect of the drops in the overall pressure-flow rate relationship.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1019 - 1028"},"PeriodicalIF":2.3,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513342","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":"Mechanical performance of negative-stiffness multistable bi-material composites","authors":"Navid Mehreganian,&nbsp;Shayan Razi,&nbsp;Arash S. Fallah,&nbsp;Pooya Sareh","doi":"10.1007/s00707-024-04158-9","DOIUrl":"10.1007/s00707-024-04158-9","url":null,"abstract":"<div><p>Architected latticed structural systems, known as metamaterials or metastructures, have recently garnered significant attention due to their superior performance under various loading conditions. This class includes metamaterials exhibiting multistability, characterized by negative stiffness, which enables energy entrapment during transitions between equilibrium states, making them suitable for applications such as lightweight protective systems. In this study, in three folds, we investigate the mechanical performance of a negative stiffness honeycomb metamaterial (NSHM) with unit cells composed of curved double beams. First, the quasi-static compressive response is numerically examined using the finite element method, revealing that this response is independent of the number of cells. Next, we analyze the transient dynamic response of both mono-material NSHMs and bi-material composites, where the stiffeners are replaced by brittle polystyrene, under localized striker and uniform plate impacts. Finally, we present an analytical model for the total potential energy, with solutions obtained through an optimization technique, and validate these results against the numerical simulations. Through these analyses, we study the effects of several parameters influencing multistability. Our findings demonstrate that the bistability ratio significantly impacts the overall response of the honeycomb, and the desired negative stiffness can be achieved with high bistability ratios. Additionally, the contact force peaks resulting from striker impact are found to be independent of the number of constituent elements. The optimized geometry of the lattice is determined through a trade-off between porosity and stiffness, achieved by thicker cell walls.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"995 - 1017"},"PeriodicalIF":2.3,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00707-024-04158-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513304","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":"Analytical solutions for bending of piezoelectric micro-beam sensors under surface stress effects","authors":"Xulong Peng,&nbsp;Jinbao Li,&nbsp;Bei Chen,&nbsp;Jin Wu,&nbsp;Zhebin Pan,&nbsp;Bing Zhao,&nbsp;Wei Li","doi":"10.1007/s00707-024-04183-8","DOIUrl":"10.1007/s00707-024-04183-8","url":null,"abstract":"<div><p>Piezoelectric sensors have been extensively utilized for the specific identification of biomolecules and the detection of chemical toxins. The optimization of piezoelectric micro-beam sensor design is crucial for applications in medical and environmental protection. This study analytically addresses the bending of piezoelectric micro-beams under surface stress by reformulating it as a plane stress problem within the framework of elasticity. A polynomial solution for stress and electric displacement is derived using the semi-inverse method for both cantilever and simply supported micro-beams. The numerical results concerning the components of stress, deflection, and electric potential are thoroughly discussed. Additionally, the influence of material parameters on the stresses, deflection, and electric potential of the piezoelectric micro-beams is examined in case of three kinds of common piezoelectric materials, thereby validating the plane-section assumption of material mechanics. The study provides theoretical guidance for the design and optimization of piezoelectric micro-beam sensors.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"983 - 994"},"PeriodicalIF":2.3,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513367","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 reduced-order model of a cantilevered extensible pipe conveying fluid: an investigation based on a consistent mass conservation approach via the extended Hamilton’s principle for nonmaterial volumes","authors":"Daniel de Oliveira Tomin,&nbsp;Renato Maia Matarazzo Orsino,&nbsp;Celso Pupo Pesce","doi":"10.1007/s00707-024-04187-4","DOIUrl":"10.1007/s00707-024-04187-4","url":null,"abstract":"<div><p>The oscillatory motion in flexible pipes due to internal flow constitutes one of the classical problems of fluid–structure interactions. Studies on the pipe dynamics must consider two features: (i) they are open systems, in which there is mass exchange through its boundaries, and (ii) the existence of dynamic instabilities, so there is a critical internal flow velocity above which the system becomes unstable. In this work, a nonlinear reduced-order model of a planar cantilevered pipe conveying fluid is derived via the extended Hamilton’s principle for nonmaterial volumes. The derivation considers the influence that the axial strain rate of the pipe must have in the internal plug flow velocity so that the proposed model becomes fully consistent in terms of conservation of mass. This condition makes the relative velocity of the flow explicitly dependent, not only on the instantaneous configuration of the pipe, but also on its rate of change, leading to the emergence of new terms in the equations of motion. Within the formalism of the extended Hamilton’s principle for nonmaterial volumes, some of these terms can be interpreted as being related to the “transport of kinetic energy”, which has not been discussed in previous studies. In order to assess the dynamic behavior of the proposed model, root loci graphs and parametric diagrams are obtained and comparisons are performed with selected models found in the literature. Also, the resulting nonlinear equations of motion are numerically integrated to show the dynamic behavior predicted by the linear analysis.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"959 - 981"},"PeriodicalIF":2.3,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513096","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":"Thermal characteristics of a multilayered annular disk with thermosensitive features using a fractional-order heat conduction model","authors":"N. K. Lamba,&nbsp;V. R. Manthena,&nbsp;P. P. Bhad,&nbsp;V. B. Srinivas,&nbsp;Ahmed E. Abouelregal","doi":"10.1007/s00707-024-04184-7","DOIUrl":"10.1007/s00707-024-04184-7","url":null,"abstract":"<div><p>The fractional theory addresses microscopic physical processes and predicts delayed responses to stimuli observed in nature. This study establishes a mathematical model that incorporates the non-local Caputo-type temporal fractional-order derivative in the heat conduction equation to analyze the thermal behavior of a thermosensitive multilayered annular disk. The disk’s inner and outer layers are subjected to convective heat exchange constraints to emphasize the significance of the fractional framework. Using Kirchhoff’s variable transformation and considering the material’s inherent thermal nonlinearity, the equations are linearized. The resulting linear equations are solved using the integral transformation method to derive mathematical expressions for deflection, resultant forces, shear forces, resultant moments, and thermal stresses. Finally, a three-layered disk composed of copper, zinc, and aluminum is constructed for numerical calculations using a fractional-ordered thermosensitive structure, enabling graphical representation of how various fractional parameters influence temperature and thermal fluctuations.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"937 - 958"},"PeriodicalIF":2.3,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513431","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":"Mechanical properties and crack extension of nanocolumnar polycrystalline copper with grain boundary segregation","authors":"Jie Wang,&nbsp;Lingfeng Mou,&nbsp;Liangfei Gong,&nbsp;Yaoyuan Liang,&nbsp;A. Mei","doi":"10.1007/s00707-024-04179-4","DOIUrl":"10.1007/s00707-024-04179-4","url":null,"abstract":"<div><p>A nanocolumnar polycrystalline copper (NCPC) model containing prefabricated cracks with random grain orientation is constructed and modified with a high-entropy grain boundary. The effects of crack length, location, and grain boundary modification on the tensile mechanical properties and crack extension behavior of NCPC are investigated by uniaxial tensile simulation by LAMMPS. Once the crack length exceeds 1 nm (limiting threshold), the peak stress in NCPC decreases significantly with increasing prefabricated crack length. Peak stress and yield limit of NCPC are dramatically enhanced after high-entropy grain boundary modification. High initial dislocation density and strong dislocation pinning due to the high-entropy grain boundaries significantly enhance the tensile mechanical properties of NCPC. The crack extension rate of high-entropy grain boundary-modified polycrystalline copper is faster than that of NCPC, and there is a more obvious difference in the crack growth evolution. The crack extension of high-entropy grain boundary-modified polycrystalline copper is mainly driven by grain boundary slip, which leads to the extension along the direction of an “X-type” shear band, while the crack extension of NCPC consists of a combination of grain dislocations and grain boundary slip.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"855 - 869"},"PeriodicalIF":2.3,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513423","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 novel gradient method for extracting elastoplastic properties of metals from spherical indentation force-contact radius data","authors":"Alaa Albayda,&nbsp;Olivier Bartier,&nbsp;Xavier Hernot,&nbsp;Gerard Mauvoisin","doi":"10.1007/s00707-024-04185-6","DOIUrl":"10.1007/s00707-024-04185-6","url":null,"abstract":"<div><p>A new methodology for determining the representative strain in spherical indentation is presented in this paper. This methodology is based on the one defined by Hernot et al. (Mech. Mater. 68:1-14, 2014) for the case of Vickers indentation. It consists in calculating the gradients of a measured quantity according to the mechanical parameters of the behavior law of the tested material. The application of the proposed method is performed based on a new numerical approach to spherical indentation. From the representative strain and stress values obtained, it can be concluded that there is no constant universal constraint factor independent of the dimensionless ratio (<i>a</i>/<i>R</i>) and the properties of the indented material. In the case of an experimental application, these representative strain and stress values allow obtaining a strain hardening curve very close to the one obtained classically by a tensile test.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"915 - 935"},"PeriodicalIF":2.3,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513421","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}