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

Author: Grafiati

Published: 6 September 2023

Last updated: 19 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Zu, J. W. Z., and R. P. S. Han. "Dynamic Response of a Spinning Timoshenko Beam With General Boundary Conditions and Subjected to a Moving Load." Journal of Applied Mechanics 61, no. 1 (1994): 152–60. http://dx.doi.org/10.1115/1.2901390.

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The dynamic response of a spinning Timoshenko beam with general boundary conditions and subjected to a moving load is solved analytically for the first time. Solution of the problem is achieved by formulating the spinning Timoshenko beams as a non-self-adjoint system. To compute the system dynamic response using the modal analysis technique, it is necessary to determine the eigenquantities of both the original and adjoint systems. In order to fix the adjoint eigenvectors relative to the eigenvectors of the original system, the biorthonormality conditions are invoked. Responses for the four cla

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12

Akgöz, Bekir, and Ömer Civalek. "Buckling Analysis of Functionally Graded Tapered Microbeams via Rayleigh–Ritz Method." Mathematics 10, no. 23 (2022): 4429. http://dx.doi.org/10.3390/math10234429.

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In the present study, the buckling problem of nonhomogeneous microbeams with a variable cross-section is analyzed. The microcolumn considered in this study is made of functionally graded materials in the longitudinal direction and the cross-section of the microcolumn varies continuously throughout the axial direction. The Bernoulli–Euler beam theory in conjunction with modified strain gradient theory are employed to model the structure by considering the size effect. The Rayleigh–Ritz numerical solution method is used to solve the eigenvalue problem for various conditions. The influences of ch

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13

Yang, Zhenghao, Konstantin Naumenko, Chien-Ching Ma, and Yang Chen. "Closed-Form Analytical Solutions for the Deflection of Elastic Beams in a Peridynamic Framework." Applied Sciences 13, no. 18 (2023): 10025. http://dx.doi.org/10.3390/app131810025.

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Peridynamics is a continuum theory that operates with non-local deformation measures as well as long-range internal force/moment interactions. The resulting equations are of the integral type, in contrast to the classical theory, which deals with differential equations. The aim of this paper is to analyze peridynamic governing equations for elastic beams. To this end, the strain energy density is formulated as a function of the non-local curvature. By applying the Lagrange principle, the peridynamic equations of motion are derived. Examples of non-local boundary conditions, including simple su

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14

Esfahanian, V., E. Dehdashti, and A. M. Dehrouyeh-Semnani. "Fluid-Structure Interaction in Microchannel Using Lattice Boltzmann Method and Size-Dependent Beam Element." Advances in Applied Mathematics and Mechanics 6, no. 3 (2014): 345–58. http://dx.doi.org/10.4208/aamm.2013.m152.

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AbstractFluid-structure interaction (FSI) problems in microchannels play prominent roles in many engineering applications. The present study is an effort towards the simulation of flow in microchannel considering FSI. Top boundary of the microchannel is assumed to be rigid and the bottom boundary, which is modeled as a Bernoulli-Euler beam, is simulated by size-dependent beam elements for finite element method (FEM) based on a modified couple stress theory. The lattice Boltzmann method (LBM) using D2Q13 LB model is coupled to the FEM in order to solve fluid part of FSI problem. In the present

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15

Fakhreddine, Hatim, Ahmed Adri, Saïd Rifai, and Rhali Benamar. "Nonlinear free and forced vibration of Euler-Bernoulli beams resting on intermediate flexible supports." MATEC Web of Conferences 211 (2018): 02003. http://dx.doi.org/10.1051/matecconf/201821102003.

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This paper deals with the geometrically nonlinear free and forced vibration analysis of a multi-span Euler Bernoulli beam resting on arbitrary number N of flexible supports, denoted as BNIFS, with general end conditions. The generality of the approach is based on use of translational and rotational springs at both ends, allowing examination of all possible combinations of classical beam end conditions, as well as elastic restraints. First, the linear case is examined to obtain the mode shapes used as trial functions in the nonlinear analysis. The beam bending vibration equation is first writte

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16

Ziou, Hassina, and Mohamed Guenfoud. "MODAL BEHAVIOUR OF LONGITUDINALLY PERFORATED NANOBEAMS." Advances in Civil and Architectural Engineering 14, no. 27 (2023): 143–59. http://dx.doi.org/10.13167/2023.27.10.

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Nano-electro-mechanical systems (NEMS) require perforated beams for structural integrity. Hole sizes, hole numbers, and scale effects need to be modelled appropriately in their design. This paper presents a new finite element model to investigate the modal behaviour of longitudinally perforated nanobeams (LPNBs) using the classical Euler–Bernoulli beam theory. A symmetric array of holes arranged parallel to the length direction of the beam with equal spacing was assumed for the perforation. The non-local Eringen’s differential form was used to incorporate the nanoscale sizes. The accuracy of t

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17

Hosseini, Mohammad, Reza Bahaadini, and Zahra Khalili-Parizi. "Structural instability of non-conservative functionally graded micro-beams tunable with piezoelectric layers." Journal of Intelligent Material Systems and Structures 30, no. 4 (2019): 593–605. http://dx.doi.org/10.1177/1045389x18818769.

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This investigation aims to explore the non-conservative instability of a functionally graded material micro-beam subjected to a subtangential force. The functionally graded material micro-beam is integrated with piezoelectric layers on the lower and upper surfaces. To take size effect into account, the mathematical derivations are expanded in terms of three length scale parameters using the modified strain gradient theory in conjunction with the Euler–Bernoulli beam model. However, the modified strain gradient theory includes modified couple stress theory and classical theory as special cases.

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18

Tanaka, N., and Y. Kikushima. "Optimal Vibration Feedback Control of an Euler-Bernoulli Beam: Toward Realization of the Active Sink Method." Journal of Vibration and Acoustics 121, no. 2 (1999): 174–82. http://dx.doi.org/10.1115/1.2893961.

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This paper discusses the optimal vibration feedback control of an Euler-Bernoulli beam from a viewpoint of active wave control making all structural modes inactive (more than suppressed). Using a transfer matrix method, the paper derives two kinds of optimal control laws termed “active sink” which inactivates all structural modes; one obtained by eliminating reflected waves and the other by transmitted waves at a control point. Moreover, the characteristic equation of the active sink system is derived, the fundamental properties being investigated. Towards the goal of implementing the optimal

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19

Bobková, Michaela, and Lukáš Pospíšil. "Numerical Solution of Bending of the Beam with Given Friction." Mathematics 9, no. 8 (2021): 898. http://dx.doi.org/10.3390/math9080898.

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We are interested in a contact problem for a thin fixed beam with an internal point obstacle with possible rotation and shift depending on a given swivel and sliding friction. This problem belongs to the most basic practical problems in, for instance, the contact mechanics in the sustainable building construction design. The analysis and the practical solution plays a crucial role in the process and cannot be ignored. In this paper, we consider the classical Euler–Bernoulli beam model, which we formulate, analyze, and numerically solve. The objective function of the corresponding optimization

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20

Montseny, Gérard. "Diffusive wave-absorbing control: example of the boundary stabilization of a thin flexible beam." Journal of Vibration and Control 18, no. 11 (2011): 1708–21. http://dx.doi.org/10.1177/1077546311419933.

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In this paper we deal with the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Such controls are based upon the reduction of reflected waves and involve long memory non-rational convolution operators resulting from specific properties of the system. These operators are reformulated under so-called diffusive input–output state-space realizations, which allow us to represent the global closed-loop system under the abstract form d X/d t = A X with A the infinitesimal generator of a continuous semigroup. So, well-posedness and stability of the controlled system re

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21

Attia, Mohamed A., and Salwa A. Mohamed. "Pull-In Instability of Functionally Graded Cantilever Nanoactuators Incorporating Effects of Microstructure, Surface Energy and Intermolecular Forces." International Journal of Applied Mechanics 10, no. 08 (2018): 1850091. http://dx.doi.org/10.1142/s1758825118500916.

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In this paper, an integrated non-classical continuum model is developed to investigate the pull-in instability of electrostatically actuated functionally graded nanocantilevers. The model accounts for the simultaneous effects of local-microstructure, surface elasticity and surface residual in the presence of fringing field as well as Casimir and van der Waals forces. The modified couple stress and Gurtin–Murdoch surface elasticity theories are employed to conduct the scaling effects of microstructure and surface energy, respectively, in the context of Euler–Bernoulli beam hypothesis. Bulk and

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22

Wakshume, Demeke Girma, and Marek Łukasz Płaczek. "Mathematical Modeling and Finite Element Simulation of the M8514-P2 Composite Piezoelectric Transducer for Energy Harvesting." Sensors 25, no. 10 (2025): 3071. https://doi.org/10.3390/s25103071.

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This paper focuses on the mathematical and numerical modeling of a non-classical macro fiber composite (MFC) piezoelectric transducer, MFC-P2, integrated with an aluminum cantilever beam for energy harvesting applications. It seeks to harness the transverse vibration energy in the environment to power small electronic devices, such as wireless sensors, where conventional power sources are inconvenient. The P2-type macro fiber composites (MFC-P2) are specifically designed for transverse energy harvesting applications. They offer high electric source capacitance and improved electric charge gene

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23

Makkad, Gulshan, Lalsingh Khalsa, and Vinod Varghese. "Fractional thermoviscoelastic damping response in a non-simple micro-beam via DPL and KG nonlocality effect." Scientific Temper 16, no. 04 (2025): 4151–64. https://doi.org/10.58414/scientifictemper.2025.16.4.18.

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This study introduces a novel framework for investigating thermoelastic damping (TED) in viscoelastic micro-scale rectangular beams using the Euler-Bernoulli beam theory (EBBT). A two-temperature thermoviscoelastic model is developed, uniquely integrating non-Fourier effects and fractional-order parameters through a generalized thermoelasticity approach with an internal heat source and the dual-phase-lag (DPL) thermal conduction model. This innovative approach addresses the limitations of classical models by incorporating size-dependent effects and spatially varying thermal properties, providi

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24

Rahmanian, Sasan, Shahrokh Hosseini-Hashemi, and Mohammad-Reza Ghazavi. "Analytical Primary Resonance of Size-Dependent Electrostatically Actuated Nanoresonator Under the Effects of Surface Energy and Casmir Force." International Journal of Applied Mechanics 11, no. 01 (2019): 1950002. http://dx.doi.org/10.1142/s1758825119500029.

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This paper investigates the nonlinear vibration of a size-dependent doubly clamped nanoresonator based on modified indeterminate couple-stress theory and Euler–Bernoulli beam theory. Surface effects, dispersion Casimir force, and fringing field effects are considered in the nonlinear model. The electrostatic actuation is a combination of DC and AC voltages and imposed on the nanobeam through one electrode. The governing differential equation of motion is derived using the extended Hamilton’s principle and discretized to a nonlinear ODE using Galerkin’s procedure. The multiple time scale method

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25

Limkatanyu, Suchart, Worathep Sae-Long, Jaroon Rungamornrat, et al. "BENDING, BUCKLING AND FREE VIBRATION ANALYSES OF NANOBEAM-SUBSTRATE MEDIUM SYSTEMS." Facta Universitatis, Series: Mechanical Engineering 20, no. 3 (2022): 561. http://dx.doi.org/10.22190/fume220506029l.

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This study presents a newly developed size-dependent beam-substrate medium model for bending, buckling, and free-vibration analyses of nanobeams resting on elastic substrate media. The Euler-Bernoulli beam theory describes the beam-section kinematics and the Winkler-foundation model represents interaction between the beam and its underlying substrate medium. The reformulated strain-gradient elasticity theory possessing three non-classical material constants is employed to address the beam-bulk material small-scale effect. The first and second constants is associated with the strain-gradient an

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26

Abouelregal, Ahmed E., Khalil M. Khalil, Wael W. Mohammed, and Doaa Atta. "Thermal vibration in rotating nanobeams with temperature-dependent due to exposure to laser irradiation." AIMS Mathematics 7, no. 4 (2022): 6128–52. http://dx.doi.org/10.3934/math.2022341.

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<abstract> <p>Effective classical representations of heterogeneous systems fail to have an effect on the overall response of components on the spatial scale of heterogeneity. This effect may be critical if the effective continuum subjects' scale differs from the material's microstructure scale and then leads to size-dependent effects and other deviations from conventional theories. This paper is concerned with the thermoelastic behavior of rotating nanoscale beams subjected to thermal loading under mechanical thermal loads based on the non-local strain gradient theory (NSGT). Also,

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27

Hosseini-Hashemi, Kamiar, Roohollah Talebitooti, and Shahriar Hosseini-Hashemi. "The exact characteristic equation of frequency and mode shape for transverse vibrations of non-uniform and non-homogeneous Euler Bernoulli beam with general non-classical boundary conditions at both ends." Mechanic of Advanced and Smart Materials 3, no. 1 (2023): 1–20. http://dx.doi.org/10.61186/masm.3.1.1.

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28

Alimoradzadeh, Mehdi, Mehdi Salehi, and Sattar Mohammadi Esfarjani. "Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory." Periodica Polytechnica Mechanical Engineering 64, no. 2 (2020): 97–108. http://dx.doi.org/10.3311/ppme.11684.

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In this study, a non-classical approach was developed to analyze nonlinear free and forced vibration of an Axially Functionally Graded (AFG) microbeam by means of modified couple stress theory. The beam is considered as Euler-Bernoulli type supported on a three-layered elastic foundation with Von-Karman geometric nonlinearity. Small size effects included in the analysis by considering the length scale parameter. It is assumed that the mass density and elasticity modulus varies continuously in the axial direction according to the power law form. Hamilton's principle was implemented to derive th

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29

Vatankhah, Ramin, Ali Najafi, Hassan Salarieh, and Aria Alasty. "Exact boundary controllability of vibrating non-classical Euler–Bernoulli micro-scale beams." Journal of Mathematical Analysis and Applications 418, no. 2 (2014): 985–97. http://dx.doi.org/10.1016/j.jmaa.2014.03.012.

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30

Sinira, B. G., B. B. Özhanb, and J. N. Reddyc. "Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supports." Latin American Journal of Solids and Structures 11, no. 14 (2014): 2516–36. http://dx.doi.org/10.1590/s1679-78252014001400010.

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31

Hrytsyna, Olha. "Local gradient Bernoulli–Euler beam model for dielectrics: effect of local mass displacement on coupled fields." Mathematics and Mechanics of Solids, October 19, 2020, 108128652096337. http://dx.doi.org/10.1177/1081286520963374.

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The size-dependent behaviour of a Bernoulli–Euler nanobeam based on the local gradient theory of dielectrics is investigated. By using the variational principle, the linear stationary governing equations of the local gradient beam model and corresponding boundary conditions are derived. In this set of equations the coupling between the strain, the electric field and the local mass displacement is taken into account. Within the presented theory, the process of local mass displacement is associated with the non-diffusive and non-convective mass flux related to the changes in the material microst

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32

Wolfgram, Zachary, and Martin Ostoja-Starzewski. "Plate and beam moment-field formulation." Mathematics and Mechanics of Solids, November 10, 2024. http://dx.doi.org/10.1177/10812865241275552.

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Governing equations of the linear elastic Euler–Bernoulli beam and pure bending Kirchhoff–Love plate are developed in a pure stress form with the evolution of the bending moments fields. In the case of elastodynamics, the governing equations are used to find mode restrictions of vibration within both structures. These vibration restrictions are then compared with the solutions found through the displacement formulation finding both forms to give the same solution under the same boundary conditions. The waves are assumed to be harmonic with only spatial contributions being examined, validating

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33

Togun, Necla, and Süleyman M. Bağdatli. "Application of Modified Couple-Stress Theory to Nonlinear Vibration Analysis of Nanobeam with Different Boundary Conditions." Journal of Vibration Engineering & Technologies, March 31, 2024. http://dx.doi.org/10.1007/s42417-024-01294-3.

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Abstract Purpose In the present study, the nonlinear vibration analysis of a nanoscale beam with different boundary conditions named as simply supported, clamped-clamped, clamped-simple and clamped-free are investigated numerically. Methods Nanoscale beam is considered as Euler-Bernoulli beam model having size-dependent. This non-classical nanobeam model has a size dependent incorporated with the material length scale parameter. The equation of motion of the system and the related boundary conditions are derived using the modified couple stress theory and employing Hamilton’s principle. Multip

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Leslie Darien Pérez Fernández, Douglas Machado da Silva, and Julián Bravo-Castillero. "Asymptotic homogenization of a mechanical equilibrium problem of a functionally-graded Euler-Bernoulli beam with non-periodic microstructure." Ibero-Latin American Congress on Computational Methods in Engineering (CILAMCE), December 2, 2024. https://doi.org/10.55592/cilamce.v6i06.8115.

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To the best of our knowledge, the few classical applications of Keller's two-space method of non-periodic asymptotic homogenization are related to the effective behavior of heterogeneous media in the context of poroelasticity considering fluid flow and saturation. We believe that this is due to the alternative common approach of approximating random or non-periodic microstructures via the periodic replication of a representative volume element, as periodic structures are, generally speaking, much more tractable mathematically and computationally. However, more than 40 years later, a number of

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35

Banerjee, J. Ranjan, Stanislav O. Papkov, Thuc P. Vo, and Isaac Elishakoff. "Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications." Journal of Vibration and Control, October 12, 2021, 107754632110482. http://dx.doi.org/10.1177/10775463211048272.

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Several models within the framework of continuum mechanics have been proposed over the years to solve the free vibration problem of micro beams. Foremost amongst these are those based on non-local elasticity, classical couple stress, gradient elasticity and modified couple stress theories. Many of these models retain the basic features of the Bernoulli–Euler or Timoshenko–Ehrenfest theories, but they introduce one or more material scale length parameters to tackle the problem. The work described in this paper deals with the free vibration problems of micro beams based on the dynamic stiffness

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36

Warminski, Jerzy, Lukasz Kloda, Jaroslaw Latalski, Andrzej Mitura, and Marcin Kowalczuk. "Nonlinear vibrations and time delay control of an extensible slowly rotating beam." Nonlinear Dynamics, December 29, 2020. http://dx.doi.org/10.1007/s11071-020-06079-3.

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AbstractNonlinear dynamics of a rotating flexible slender beam with embedded active elements is studied in the paper. Mathematical model of the structure considers possible moderate oscillations thus the motion is governed by the extended Euler–Bernoulli model that incorporates a nonlinear curvature and coupled transversal–longitudinal deformations. The Hamilton’s principle of least action is applied to derive a system of nonlinear coupled partial differential equations (PDEs) of motion. The embedded active elements are used to control or reduce beam oscillations for various dynamical conditio

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37

Mohammad, Roslina, Astuty Amrin, and Sallehuddin Muhamad. "THEORETICAL OF DYNAMIC LOADING AGAINST WATER-FILLED SIMPLY SUPPORTED PIPES." Jurnal Teknologi 75, no. 11 (2015). http://dx.doi.org/10.11113/jt.v75.5343.

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The primary aim of this study had been to investigate the effects of water-filled flow on the transient response of a simply supported pipe subjected to dynamically applied loading. The importance of this study is manifested in numerous applications, such as oil and gas transportations, where dynamic loading can be the result of an accident. The classical Bernoulli-Euler beam theory was adopted to describe the dynamic behavior of an elastic pipe and a new governing equation of a long pipe transporting gas or liquid was derived. This governing equation incorporated the effects of inertia, centr

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38

Afras, Abderrachid, and Abdelouafi El Ghoulbzouri. "Effects of non-classical boundary conditions on the free vibration response of a cantilever Euler-Bernoulli beams." Diagnostyka, January 4, 2023, 1–13. http://dx.doi.org/10.29354/diag/158075.

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