Relevant bibliographies by topics / Euler-Bernoulli beam equation

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Academic literature on the topic 'Euler-Bernoulli beam equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Euler-Bernoulli beam equation"

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LIM, TEIK-CHENG. "ANALYSIS OF AUXETIC BEAMS AS RESONANT FREQUENCY BIOSENSORS." Journal of Mechanics in Medicine and Biology 12, no. 05 (2012): 1240027. http://dx.doi.org/10.1142/s0219519412400271.

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The mechanics of beam vibration is of fundamental importance in understanding the shift of resonant frequency of microcantilever and nanocantilever sensors. Unlike the simpler Euler–Bernoulli beam theory, the Timoshenko beam theory takes into consideration rotational inertia and shear deformation. For the case of microcantilevers and nanocantilevers, the minute size, and hence low mass, means that the topmost deviation from the Euler–Bernoulli beam theory to be expected is shear deformation. This paper considers the extent of shear deformation for varying Poisson's ratio of the beam material,
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Naz, R., and F. M. Mahomed. "Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/520491.

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We study a dynamic fourth-order Euler-Bernoulli partial differential equation having a constant elastic modulus and area moment of inertia, a variable lineal mass densityg(x), and the applied load denoted byf(u), a function of transverse displacementu(t,x). The complete Lie group classification is obtained for different forms of the variable lineal mass densityg(x)and applied loadf(u). The equivalence transformations are constructed to simplify the determining equations for the symmetries. The principal algebra is one-dimensional and it extends to two- and three-dimensional algebras for an arb
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Czyczula, Wlodzimierz, Piotr Koziol, and Dorota Blaszkiewicz. "On the Equivalence between Static and Dynamic Railway Track Response and on the Euler-Bernoulli and Timoshenko Beams Analogy." Shock and Vibration 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/2701715.

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The paper tries to clarify the problem of solution and interpretation of railway track dynamics equations for linear models. Set of theorems is introduced in the paper describing two types of equivalence: between static and dynamic track response under moving load and between the dynamic response of track described by both the Euler-Bernoulli and Timoshenko beams. The equivalence is clarified in terms of mathematical method of solution. It is shown that inertia element of rail equation for the Euler-Bernoulli beam and constant distributed load can be considered as a substitute axial force mult
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Fatima, Aeeman, Fazal M. Mahomed, and Chaudry Masood Khalique. "Noether symmetries and exact solutions of an Euler–Bernoulli beam model." International Journal of Modern Physics B 30, no. 28n29 (2016): 1640011. http://dx.doi.org/10.1142/s0217979216400117.

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In this paper, a Noether symmetry analysis is carried out for an Euler–Bernoulli beam equation via the standard Lagrangian of its reduced scalar second-order equation which arises from the standard Lagrangian of the fourth-order beam equation via its Noether integrals. The Noether symmetries corresponding to the reduced equation is shown to be the inherited Noether symmetries of the standard Lagrangian of the beam equation. The corresponding Noether integrals of the reduced Euler–Lagrange equations are deduced which remarkably allows for three families of new exact solutions of the static beam
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Zhang, Jin-lun, Liao-jun Zhang, Ren-yu Ge, Li Yang, and Jun-wu Xia. "Study on Natural Frequencies of Transverse Free Vibration of Functionally Graded Axis Beams by the Differential Quadrature Method." Acta Acustica united with Acustica 105, no. 6 (2019): 1095–104. http://dx.doi.org/10.3813/aaa.919388.

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Functionally gradient materials with special mechanical characteristics are more and more widely used in engineering. The functionally graded beam is one of the commonly used components to bear forces in the structure. Accurate analysis of the dynamic characteristics of the axially functionally graded (AFG) beam plays a vital role in the design and safe operation of the whole structure. Based on the Euler-Bernoulli beam theory (EBT), the characteristic equation of transverse free vibration for the AFG Euler-Bernoulli beam with variable cross-section is obtained in the present work, and the gov
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Tekin, Ibrahim, and He Yang. "INVERSE PROBLEM FOR THE TIME-FRACTIONAL EULER-BERNOULLI BEAM EQUATION." Mathematical Modelling and Analysis 26, no. 3 (2021): 503–18. http://dx.doi.org/10.3846/mma.2021.13289.

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In this paper, the classical Euler-Bernoulli beam equation is considered by utilizing fractional calculus. Such an equation is called the time-fractional EulerBernoulli beam equation. The problem of determining the time-dependent coefficient for the fractional Euler-Bernoulli beam equation with homogeneous boundary conditions and an additional measurement is considered, and the existence and uniqueness theorem of the solution is proved by means of the contraction principle on a sufficiently small time interval. Numerical experiments are also provided to verify the theoretical findings.
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SHEN, HUI-SHEN. "A NOVEL TECHNIQUE FOR NONLINEAR ANALYSIS OF BEAMS ON TWO-PARAMETER ELASTIC FOUNDATIONS." International Journal of Structural Stability and Dynamics 11, no. 06 (2011): 999–1014. http://dx.doi.org/10.1142/s0219455411004440.

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Postbuckling, nonlinear bending, and nonlinear vibration analyses are presented for a simply supported Euler–Bernoulli beam resting on a two-parameter elastic foundation. The nonlinear model is introduced by using the exact expression of the curvature. Two kinds of end conditions, namely movable and immovable, are considered. The nonlinear equation of motion, including beam–foundation interaction, is derived separately for these two kinds of end conditions. The analysis uses a two-step perturbation technique to determine the postbuckling equilibrium paths of an axially loaded beam, the static
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Tang, Shao-Qiang, and Eduard G. Karpov. "Artificial boundary conditions for Euler-Bernoulli beam equation." Acta Mechanica Sinica 30, no. 5 (2014): 687–92. http://dx.doi.org/10.1007/s10409-014-0089-7.

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Baysal, Onur, and Alemdar Hasanov. "Solvability of the clamped Euler–Bernoulli beam equation." Applied Mathematics Letters 93 (July 2019): 85–90. http://dx.doi.org/10.1016/j.aml.2019.02.006.

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Khaldi, Rabah, and Assia Guezane-Lakoud. "On generalized nonlinear Euler-Bernoulli Beam type equations." Acta Universitatis Sapientiae, Mathematica 10, no. 1 (2018): 90–100. http://dx.doi.org/10.2478/ausm-2018-0008.

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Abstract This paper is devoted to the study of a nonlinear Euler-Bernoulli Beam type equation involving both left and right Caputo fractional derivatives. Differently from the approaches of the other papers where they established the existence of solution for the linear Euler-Bernoulli Beam type equation numerically, we use the lower and upper solutions method with some new results on the monotonicity of the right Caputo derivative. Furthermore, we give the explicit expression of the upper and lower solutions. A numerical example is given to illustrate the obtained results.
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Dissertations / Theses on the topic "Euler-Bernoulli beam equation"

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Rydström, Sara. "Regularization of Parameter Problems for Dynamic Beam Models." Licentiate thesis, Växjö University, School of Mathematics and Systems Engineering, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-7367.

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<p>The field of inverse problems is an area in applied mathematics that is of great importance in several scientific and industrial applications. Since an inverse problem is typically founded on non-linear and ill-posed models it is a very difficult problem to solve. To find a regularized solution it is crucial to have <em>a priori</em> information about the solution. Therefore, general theories are not sufficient considering new applications.</p><p>In this thesis we consider the inverse problem to determine the beam bending stiffness from measurements of the transverse dynamic displacement. O
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Evans, Katie Allison. "Reduced Order Controllers for Distributed Parameter Systems." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/11063.

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Distributed parameter systems (DPS) are systems defined on infinite dimensional spaces. This includes problems governed by partial differential equations (PDEs) and delay differential equations. In order to numerically implement a controller for a physical system we often first approximate the PDE and the PDE controller using some finite dimensional scheme. However, control design at this level will typically give rise to controllers that are inherently large-scale. This presents a challenge since we are interested in the design of robust, real-time controllers for physical systems. Therefore,
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Ndiaye, Moctar. "Stabilisation et simulation de modèles d'interaction fluide-structure." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30323/document.

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L'objet de cette thèse est l'étude de la stabilisation de modèles d'interaction fluide-structure par des contrôles de dimension finie agissant sur la frontière du domaine fluide. L'écoulement du fluide est décrit par les équations de Navier-Stokes incompressibles tandis que l'évolution de la structure, située à la frontière du domaine fluide, satisfait une équation d'Euler-Bernoulli avec amortissement. Dans le chapitre 1, nous étudions le cas où le contrôle est une condition aux limites de Dirichlet sur les équations du fluide (contrôle par soufflage/aspiration). Nous obtenons des résultats de
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Johnson, William Richard. "Active Structural Acoustic Control of Clamped and Ribbed Plates." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/4011.

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A control metric, the weighted sum of spatial gradients (WSSG), has been developed for use in active structural acoustic control (ASAC). Previous development of WSSG [1] showed that it was an effective control metric on simply supported plates, while being simpler to measure than other control metrics, such as volume velocity. The purpose of the current work is to demonstrate that the previous research can be generalized to plates with a wider variety of boundary conditions and on less ideal plates. Two classes of plates have been considered: clamped flat plates, and ribbed plates. On clamped
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Hansen, Scott Walter. "Frequency-proportional damping models for the Euler-Bernoulli beam equation." 1988. http://catalog.hathitrust.org/api/volumes/oclc/20126239.html.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1988.<br>Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 220-222).
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Chang, Bo-Jun, and 張博竣. "By Using Bounday Integral Equation Method to Solve The Direct Euler-Bernoulli Beam Problem." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/68160082120270051341.

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碩士<br>國立臺灣大學<br>土木工程學研究所<br>104<br>In this thesis we numerically solve the direct Euler-Bernoulli beam problems by using a boundary integral equation method(BIEM) which is based on the generalized Green’s second identity and the self-adjoint operators. In the BIEM, we choose a set of adjoint Trefftz test functions which can be obtained by the method of separation of variables. In the numerical algorithm, we can expand a trial solution by using the bases satisfying the homogeneous governing equation and the boundary conditions simultaneously. To satisfy the above two properties of the bases, we
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Huang, Po-Chang, and 黃柏彰. "A closed-form coefficients expansion method for recovering spatial-dependent load on the Euler-Bernoulli beam equation." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/csmb2s.

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碩士<br>國立臺灣大學<br>土木工程學研究所<br>105<br>In the field of Civil engineering, the forced vibration of a bridge is a big issue. When discussing the behavior of a bridge, we can apply the Euler-Bernoulli beam theory to analyze it simply. There are several methods to analyze the Euler-Bernoulli beam equation under an external force; however, without knowing the external force, it becomes an inverse source problem which is much more complicated.In this thesis, we adopt the boundary integral equation method (BIEM) with the mode shapes as adjoint test functions. Then, we can develop a non-iterative method
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"Numerical Solutions of Wave Propagation in Beams." Master's thesis, 2016. http://hdl.handle.net/2286/R.I.38587.

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abstract: In order to verify the dispersive nature of transverse displacement in a beam, a deep understanding of the governing partial differential equation is developed. Using the finite element method and Newmark’s method, along with Fourier transforms and other methods, the aim is to obtain consistent results across each numerical technique. An analytical solution is also analyzed for the Euler-Bernoulli beam in order to gain confidence in the numerical techniques when used for more advance beam theories that do not have a known analytical solution. Three different beam theories are analyze
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Hsu, Huan-Cheng, and 許桓誠. "By Using Boundary Integral Equation Method to Solve the Inverse Problems of Forces of Euler-Bernoulli Beams." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/39628815515428333457.

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碩士<br>國立臺灣大學<br>土木工程學研究所<br>104<br>Euler-Bernoulli beam theory is a typical beam theory when discussing the behavior of beams. There are several methods to obtain the behaviors of the Euler-Bernoulli beam under an external force, but without knowing the external force, the problem becomes an inverse source problem which is the subject of this thesis. Different from the direct problems, the inverse problems are considered more ill-posed. In this thesis, the boundary integral equations method will be adopted to solve the Euler-Bernoulli beam problem, with its mode shape as an adjoint test funct
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Mahaffey, Patrick Brian. "Bending, Vibration and Buckling Response of Conventional and Modified Euler-Bernoulli and Timoshenko Beam Theories Accounting for the von Karman Geometric Nonlinearity." Thesis, 2013. http://hdl.handle.net/1969.1/151319.

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Beams are among the most commonly used structural members that are encountered in virtually all systems of structural design at various scales. Mathematical models used to determine the response of beams under external loads are deduced from the three-dimensional elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. The kinematic assumptions exploit the fact that such structures do not experience significant trans- verse normal and shear strains and stresses. For example, the solution of the three- dimensional elasticity problem
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Books on the topic "Euler-Bernoulli beam equation"

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Smith, Ralph C. A fully Sinc-Galerkin method for Euler-Bernoulli beam models. Institute for Computer Applications in Science and Engineering, 1990.

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Book chapters on the topic "Euler-Bernoulli beam equation"

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Chen, Jingkai. "Peridynamics Beam Equation." In Nonlocal Euler–Bernoulli Beam Theories. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4_3.

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Pathak, Maheshwar, and Pratibha Joshi. "High-Order Compact Finite Difference Scheme for Euler–Bernoulli Beam Equation." In Harmony Search and Nature Inspired Optimization Algorithms. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0761-4_35.

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Ruiz, A., C. Muriel, and J. Ramírez. "Parametric Solutions to a Static Fourth-Order Euler–Bernoulli Beam Equation in Terms of Lamé Functions." In Recent Advances in Pure and Applied Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41321-7_7.

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Chen, Jingkai. "Nonlocal Beam Equations." In Nonlocal Euler–Bernoulli Beam Theories. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4_2.

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Öchsner, Andreas. "Euler–Bernoulli Beams." In Partial Differential Equations of Classical Structural Members. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-35311-7_3.

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Luo, Zheng-Hua, Bao-Zhu Guo, and Omer Morgul. "Static Sensor Feedback Stabilization of Euler-Bernoulli Beam Equations." In Stability and Stabilization of Infinite Dimensional Systems with Applications. Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0419-3_4.

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Hasanov Hasanoğlu, Alemdar, and Vladimir G. Romanov. "Inverse Problems for Euler-Bernoulli Beam and Kirchhoff Plate Equations." In Introduction to Inverse Problems for Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79427-9_11.

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Mosavi, Amir, Rami Benkreif, and Annamária R. Varkonyi-Koczy. "Comparison of Euler-Bernoulli and Timoshenko Beam Equations for Railway System Dynamics." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67459-9_5.

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"Intermediate Theory Between the Bernoulli–Euler and the Timoshenko–Ehrenfest Beam Theories: Truncated Timoshenko–Ehrenfest Equations." In Handbook on Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813236523_0003.

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Conference papers on the topic "Euler-Bernoulli beam equation"

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Xue, Hui, and H. Khawaja. "Analytical study of sandwich structures using Euler–Bernoulli beam equation." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972668.

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Guo, Bao-Zhu, and Tingting Meng. "Robust output feedback Control for an Euler-Bernoulli Beam Equation." In 2020 American Control Conference (ACC). IEEE, 2020. http://dx.doi.org/10.23919/acc45564.2020.9147416.

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Fan, W., W. D. Zhu, and H. Ren. "A New Singularity-Free Formulation of a Three-Dimensional Euler-Bernoulli Beam Using Euler Parameters." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-53365.

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In this investigation, a new singularity-free formulation of a three-dimensional Euler-Bernoulli beam with large deformation and large rotation is developed. The position of the centroid line of the beam is integrated from its slope, which can be easily expressed by Euler parameters. The hyper-spherical interpolation function is used to guarantee that the normalization constraint equation of Euler parameters is always satisfied. Hence, each node of a beam element has only four nodal coordinates, which is significantly fewer than an absolute node coordinate formulation (ANCF) and the finite ele
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Naguleswaran, S. "Vibration of an Euler-Bernoulli Uniform Beam Carrying Several Thin Disks." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48361.

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The Euler-Bernoulli uniform beam considered in this paper carry (n+1) thin disks, two of which are at the beam ends. For the analytical method used in the paper, n co-ordinate systems were chosen with origins at the disk locations. The mode shape of the portion of the beam between the jth and (j+1)th disk was expressed in the form Yj(Xj) = A Uj(Xj) + B Vj(Xj) in which Uj(Xj) and Vj(Xj) are ‘modified’ mode shape functions applicable to that portion but the constants A and B are common to all the portions. From the compatibility of moments and forces on the (n+1)th disk, the frequency equation w
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Caruntu, Dumitru I. "On Transverse Vibrations of Rotating Non-Uniform Beams." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15290.

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Several evaluations of natural frequencies of rotating structural elements such as windmill rotors, aircraft propellers, space frames and turbine blades have been published. Lateral vibration of centrifugally tensioned uniform Euler-Bernoulli beam, and transverse deflections of a straight tapered symmetric beam attached to a rotating hub as model for bending vibration of blades in turbomachinery have been reported in the literature. This paper presents the factorization of the fourth-order linear differential equation of motion of bending vibrations of rotating nonuniform Euler-Bernoulli beams
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Lu, Lu, and Jun-Min Wang. "Dynamic boundary stabilization of Euler-Bernoulli beam through a Kelvin-Voigt damped wave equation." In 2014 26th Chinese Control And Decision Conference (CCDC). IEEE, 2014. http://dx.doi.org/10.1109/ccdc.2014.6852149.

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Bao-Zhu Guo and Feng-Fei Jin. "Two approaches to the stabilization of Euler-Bernoulli beam equation with control matched disturbance." In 2013 American Control Conference (ACC). IEEE, 2013. http://dx.doi.org/10.1109/acc.2013.6580015.

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Tzes, Yurkovich, and Langer. "A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems." In IEEE International Conference on Systems Engineering. IEEE, 1989. http://dx.doi.org/10.1109/icsyse.1989.48736.

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Feng, Hongyinping, Bao-Zhu Guo, and Wei Guo. "Disturbance estimator based output feedback stabilizing control for an Euler-Bernoulli beam equation with boundary uncertainty." In 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, 2017. http://dx.doi.org/10.1109/cdc.2017.8263828.

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Guo, Bao-Zhu, and Han-Jing Ren. "Uniform Convergence for Eigenvalues of Euler-Bernoulli Beam Equation with Structural Damping via Finite Difference Discretization." In 2018 37th Chinese Control Conference (CCC). IEEE, 2018. http://dx.doi.org/10.23919/chicc.2018.8483525.

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Reports on the topic "Euler-Bernoulli beam equation"

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Chen, G., S. G. Krantz, D. W. Ma, C. E. Wayne, and H. H. West. The Euler-Bernoulli Beam Equation with Boundary Energy Dissipation. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada189517.

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