Relevant bibliographies by topics / Non-classical Euler-Bernoulli beam

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Non-classical Euler-Bernoulli beam'

Author: Grafiati
Published: 6 September 2023
Last updated: 31 July 2025

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Journal articles on the topic "Non-classical Euler-Bernoulli beam"

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Samayoa, Didier, Andriy Kryvko, Gelasio Velázquez, and Helvio Mollinedo. "Fractal Continuum Calculus of Functions on Euler-Bernoulli Beam." Fractal and Fractional 6, no. 10 (2022): 552. http://dx.doi.org/10.3390/fractalfract6100552.

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A new approach for solving the fractal Euler-Bernoulli beam equation is proposed. The mapping of fractal problems in non-differentiable fractals into the corresponding problems for the fractal continuum applying the fractal continuum calculus (FdH3-CC) is carried out. The fractal Euler-Bernoulli beam equation is derived as a generalization using FdH3-CC under analogous assumptions as in the ordinary calculus and then it is solved analytically. To validate the spatial distribution of self-similar beam response, three different classical beams with several fractal parameters are analysed. Some m
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Yin, Shuohui, Zhibing Xiao, Gongye Zhang, Jingang Liu, and Shuitao Gu. "Size-Dependent Buckling Analysis of Microbeams by an Analytical Solution and Isogeometric Analysis." Crystals 12, no. 9 (2022): 1282. http://dx.doi.org/10.3390/cryst12091282.

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This paper proposes an analytical solution and isogeometric analysis numerical approach for buckling analysis of size-dependent beams based on a reformulated strain gradient elasticity theory (RSGET). The superiority of this method is that it has only one material parameter for couple stress and another material parameter for strain gradient effects. Using the RSGET and the principle of minimum potential energy, both non-classical Euler–Bernoulli and Timoshenko beam buckling models are developed. Moreover, the obtained governing equations are solved by an exact solution and isogeometric analys
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Stempin, Paulina, and Wojciech Sumelka. "Dynamics of Space-Fractional Euler–Bernoulli and Timoshenko Beams." Materials 14, no. 8 (2021): 1817. http://dx.doi.org/10.3390/ma14081817.

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This paper investigates the dynamics of the beam-like structures whose response manifests a strong scale effect. The space-Fractional Euler–Bernoulli beam (s-FEBB) and space-Fractional Timoshenko beam (s-FTB) models, which are suitable for small-scale slender beams and small-scale thick beams, respectively, have been extended to a dynamic case. The study provides appropriate governing equations, numerical approximation, detailed analysis of free vibration, and experimental validation. The parametric study presents the influence of non-locality parameters on the frequencies and shape of modes d
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Ghorbanpourarani, A., M. Mohammadimehr, A. Arefmanesh, and A. Ghasemi. "Transverse vibration of short carbon nanotubes using cylindrical shell and beam models." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 3 (2009): 745–56. http://dx.doi.org/10.1243/09544062jmes1659.

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The transverse vibrations of single- and double-walled carbon nanotubes are investigated under axial load by applying the Euler—Bernoulli and Timoshenko beam models and the Donnell shell model. It is concluded that the Euler—Bernoulli beam model and the Donnell shell model predictions have the lowest and highest accuracies, respectively. In order to predict the vibration behaviour of the carbon nanotube more accurately, the current classical models are modified using the non-local theory. The natural frequencies, amplitude coefficient, critical axial load, and strain are obtained for the simpl
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Zhang, GY, and X.-L. Gao. "A new Bernoulli–Euler beam model based on a reformulated strain gradient elasticity theory." Mathematics and Mechanics of Solids 25, no. 3 (2019): 630–43. http://dx.doi.org/10.1177/1081286519886003.

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A new non-classical Bernoulli–Euler beam model is developed using a reformulated strain gradient elasticity theory that incorporates both couple stress and strain gradient effects. This reformulated theory is first derived from Form I of Mindlin’s general strain gradient elasticity theory. It is then applied to develop the model for Bernoulli–Euler beams through a variational formulation based on Hamilton’s principle, which leads to the simultaneous determination of the equation of motion and the complete boundary conditions and provides a unified treatment of the strain gradient, couple stres
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Ishaquddin, Md, and S. Gopalakrishnan. "Differential quadrature-based solution for non-classical Euler-Bernoulli beam theory." European Journal of Mechanics - A/Solids 86 (March 2021): 104135. http://dx.doi.org/10.1016/j.euromechsol.2020.104135.

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Mei, C. "Vibrations in a spatial K-shaped metallic frame: an exact analytical study with experimental validation." Journal of Vibration and Control 23, no. 19 (2016): 3147–61. http://dx.doi.org/10.1177/1077546315627085.

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In a spatial K-shaped metallic frame, there exist in- and out-of-plane bending, axial, and torsional vibrations. A wave-based vibration analysis approach is applied to obtain free and forced vibration responses in a space frame. In order to validate the analytical approach, a steel K-shaped space frame was built by welding four beam elements of rectangular and square cross-section together. Bending vibrations are modeled using both the classical Euler–Bernoulli theory and the advanced Timoshenko theory. This allows the effects of rotary inertia and shear distortion, which were neglected in the
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König, Paul, Patrick Salcher, Christoph Adam, and Benjamin Hirzinger. "Dynamic analysis of railway bridges exposed to high-speed trains considering the vehicle–track–bridge–soil interaction." Acta Mechanica 232, no. 11 (2021): 4583–608. http://dx.doi.org/10.1007/s00707-021-03079-1.

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AbstractA new semi-analytical approach to analyze the dynamic response of railway bridges subjected to high-speed trains is presented. The bridge is modeled as an Euler–Bernoulli beam on viscoelastic supports that account for the flexibility and damping of the underlying soil. The track is represented by an Euler–Bernoulli beam on viscoelastic bedding. Complex modal expansion of the bridge and track models is performed considering non-classical damping, and coupling of the two subsystems is achieved by component mode synthesis (CMS). The resulting system of equations is coupled with a moving m
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Zhang, G. Y., X. L. Gao, C. Y. Zheng, and C. W. Mi. "A non-classical Bernoulli-Euler beam model based on a simplified micromorphic elasticity theory." Mechanics of Materials 161 (October 2021): 103967. http://dx.doi.org/10.1016/j.mechmat.2021.103967.

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Yin, Shuohui, Yang Deng, Tiantang Yu, Shuitao Gu, and Gongye Zhang. "Isogeometric analysis for non-classical Bernoulli-Euler beam model incorporating microstructure and surface energy effects." Applied Mathematical Modelling 89 (January 2021): 470–85. http://dx.doi.org/10.1016/j.apm.2020.07.015.

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Dissertations / Theses on the topic "Non-classical Euler-Bernoulli beam"

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Migotto, Dionéia. "Autofunções e Frequências de Vibração do Modelo Euler-Bernoulli para Vigas Não-Clássicas." Universidade Federal de Santa Maria, 2011. http://repositorio.ufsm.br/handle/1/9971.

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This paper presents a methodology for determining eigenfunctions and frequencies of the Euler-Bernoulli model for elastic beams that can include damping and devices located at intermediate or end points of the beam. The eigenfunctions or vibration modes of the beam are obtained by using solution basis generated by the dynamic solution of a fourth-order differential equation, through a block matrix formulation of the boundary and compatibility conditions. The use of the dynamic basis has been often used to reduce the calculations in obtaining the modes and frequencies. Forced responses are obta
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Ishaquddin, Mohammed. "Numerical solution of non-classical beam and plate theories using di erential quadrature method." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/4586.

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For effcient design of the nano/micro scale structural systems, detailed analysis and through understanding of size-dependent mechanical behaviour at nano/micro scale is very critical. Various approaches have been used to investigate the mechanical behaviour of small scale structures, for instance, experimental approach, atomistic and molecular dynamics simulations, multi-scale modelling, etc. However, the application of these methods for practical problems have their own limitations, some are very cumbersome and expensive, others need high computational resources and remaining are mathe
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Book chapters on the topic "Non-classical Euler-Bernoulli beam"

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Feklistova Ljubov and Hein Helle. "Parameter identification for supports and cracks in beams with non-classical boundary conditions." In Construction Materials and Structures. IOS Press, 2014. https://doi.org/10.3233/978-1-61499-466-4-1295.

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This article addresses parameter identification problem in vibrating Euler-Bernoulli beams with an open crack or elastic intermediate supports. The crack is simulated by a line spring model. The boundary value problem is solved by the aid of Haar wavelets. The characteristic parameters are predicted using the artificial neural networks. Two different approaches based on natural frequencies and Haar wavelets are compared. The significance of the second approach lies in its ability to make fast and trustworthy predictions on the selected parameters.
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Conference papers on the topic "Non-classical Euler-Bernoulli beam"

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Claeyssen, Julio R., Rosemaira Dalcin Copetti, and Teresa Tsukazan. "Matrix Vibration Formulation of Damped Multi-Span Beams." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14933.

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In this work we consider segmented Euler-Bernoulli beams that can have an internal damping of the type Kelvin-Voight and external viscous damping at the discontinuities of the sections. In the literature, the study of this kind of beams has been sufficiently studied with proportional damping only, however the effects of non-proportional damping has been little studied in terms of modal analysis. The obtaining of the modes of segmented beams can be accomplished with a the state space methodology or with the classical Euler construction of responses. Here, we follow a newtonian approach with the
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Taati, E., M. Nikfar, and M. T. Ahmadian. "Formulation for Static Behavior of the Viscoelastic Euler-Bernoulli Micro-Beam Based on the Modified Couple Stress Theory." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-86591.

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In this work an analytical solution is presented for a viscoelastic micro-beam based on the modified couple stress theory which is a non-classical theory in continuum mechanics. The modified couple stress theory has the ability to consider small size effects in micro-structures. It is strongly emphasized that without considering these effects in such structures the solution will be wrong and not suitable for designing systems in micro-scales. In this study correspondence principle is used for deriving constitutive equations for viscoelastic material based on the modified couple stress theory.
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Cuhat, Daniel, and Patricia Davies. "An Experimental Approach to the Design of PVDF Modal Sensors." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21537.

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Abstract The principle of modal sensing is based on the use of a shaped PVDF piezoelectric film measuring strains on the surface of a bending beam and acting as a modal filter. So far, the use of this type of sensors has remained confined to studies involving uniform structures with classical boundary conditions. The goal of this paper is to present an experimental methodology for the design of a shaped modal sensor applicable to an non-uniform Euler-Bernoulli beam with arbitrary boundary conditions. This approach is illustrated with test data collected on a cantilever beam structure with a la
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Kheiri, Mojtaba, Michael P. Païdoussis, and Giorgio Costa del Pozo. "Dynamics of a Pipe Conveying Fluid Flexibly Supported at the Ends." In ASME 2014 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/pvp2014-28335.

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The subject of this paper is the study of dynamics and stability of a pipe flexibly supported at its ends and conveying fluid. First, the equation of motion of the system is derived via the extended form of Hamilton’s principle for open systems. In the derivation, the effect of flexible supports, modelled as linear translational and rotational springs, is appropriately considered in the equation of motion rather than in the boundary conditions. The resulting equation of motion is then discretized via the Galerkin method in which the eigenfunctions of a free-free Euler-Bernoulli beam are utiliz
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Saadatnia, Zia, and Ebrahim Esmailzadeh. "Nonlinear Forced Vibration Analysis of a Non-Local Carbon Nanotube Carrying Intermediate Mass." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46855.

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The aim of this study is to model and investigate the nonlinear transversal vibration of a carbon nanotube carrying an intermediate mass along the structure considering the nonlocal and non-classical theories. Due to the application of the proposed system in sensors, actuators, mass detection units among others, the analysis of forced vibration of such systems is of an important task being considered here. The governing equation of motion is developed by combining the Euler-Bernoulli beam theory and the Eringen non-local theory. The Galerkin approach is employed to obtain the governing differe
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Boivin, Nicolas, Christophe Pierre, and Steven W. Shaw. "Non-Linear Normal Modes, Invariance, and Modal Dynamics Approximations of Non-Linear Systems." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0028.

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Abstract Non-linear systems are here tackled in a manner directly inherited from linear ones, i.e., by denning proper normal modes of motion. These are defined in terms of invariant manifolds in the system’s phase space, on which the uncoupled system dynamics can be studied. Two different methodologies which were previously developed to derive the non-linear normal modes of continuous systems — one based on a purely continuous approach, and one based on a discretized approach where the theory developed for discrete systems can be applied — are simultaneously applied to the same study case — an
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João Fernandes da Silva, Lucas Allende Dias do Nascimento, and Simone dos Santos Hoefel. "Free vibration analysis of Euler-Bernoulli beams under non-classical boundary conditions." In IX Congresso Nacional de Engenharia Mecânica. ABCM Associação Brasileira de Engenharia e Ciências Mecânicas, 2016. http://dx.doi.org/10.20906/cps/con-2016-1053.

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Chen, Boyang, Simon Jones, and Matt Riley. "Stochastic Finite Element Modeling of Laminated Fiber-Reinforced Composite Beams Under Transverse Loading." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-69851.

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Abstract It is common in analytic fiber-reinforced composite theory to assume uniformly distributed material properties across the fiber direction to minimize computational expense. However, manufacturing processes introduce imperfections during the construction of composite materials, such as localized delamination, non-uniform distribution in matrix and fibers, pre-existing stress, and tolerance issues [1]. These imperfections make it more difficult to predict the behavior of composite materials under loading. As a result, manufacturers and designers must use conservative estimates of materi
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Nunes, Afonso Willian, Samuel da Silva, Paulo Gonçalves, and Jean-Mathieu Mencik. "Stable computation of mode shapes of uniform Euler-Bernoulli beams subject to classical and non-classical boundary conditions via Lie symmetries." In 8th International Symposium on Solid Mechanics. ABCM, 2022. http://dx.doi.org/10.26678/abcm.mecsol2022.msl22-0132.

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