Results 11 to 20 of about 3,266 (209)

Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance

Journal of Hebei University of Science and Technology, 2017
In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied.
Pengcheng HAN, Danhong LIU
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Vibration modes of the Euler–Bernoulli beam equation with singularities

Journal of Differential Equations
We consider the time dependent Euler--Bernoulli beam equation with discontinuous and singular coefficients. Using an extension of the Hörmander product of distributions with non-intersecting singular supports [L. Hörmander, The Analysis of Linear Partial Diffe\-rential Operators I, Springer-Verlag, 1983], we obtain an explicit formulation of the ...
Nuno Costa Dias, Cristina Jorge, João Nuno Prata   +2 more
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Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions [PDF]

Mathematical Problems in Engineering, 2015
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).
Naz, R., Mahomed, F.M.
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Gevrey regularity for the Euler–Bernoulli beam equation with localized structural damping

Applicable Analysis, 2023
We study a Euler-Bernoulli beam equation with localized discontinuous structural damping. As our main result, we prove that the associated $C_0$-semigroup $(S(t))_{t\geq0}$ is of Gevrey class $δ>24$ for $t>0$, hence immediately differentiable. Moreover, we show that $(S(t))_{t\geq0}$ is exponentially stable.
Caggio, Matteo, Dell'Oro, Filippo
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Influence of Material Defects on the Dynamic Stability of the Bernoulli-Euler Beam [PDF]

Archives of Metallurgy and Materials, 2021
The paper presents the results of tests on dynamic stability of Bernoulli-Euler beam with damages. Damages (cracks) were modeled using three rotational springs.
W. Sochacki, S. Garus, J. Garus
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Analytical study of sandwich structures using Euler–Bernoulli beam equation [PDF]

AIP Conference Proceedings, 2017
This paper presents an analytical study of sandwich structures. In this study, the Euler–Bernoulli beam equation is solved analytically for a four-point bending problem. Appropriate initial and boundary conditions are specified to enclose the problem. In addition, the balance coefficient is calculated and the Rule of Mixtures is applied.
Xue, Hui, Khawaja, Hassan Abbas
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On the spectrum of Euler–Bernoulli beam equation with Kelvin–Voigt damping

Journal of Mathematical Analysis and Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Guo-Dong, Guo, Bao-Zhu
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An Efficient Petrov–Galerkin Scheme for the Euler–Bernoulli Beam Equation via Second-Kind Chebyshev Polynomials

Fractal and Fractional
The current article introduces a Petrov–Galerkin method (PGM) to address the fourth-order uniform Euler–Bernoulli pinned–pinned beam equation. Utilizing a suitable combination of second-kind Chebyshev polynomials as a basis in spatial variables, the ...
Youssri Hassan Youssri, Waleed Mohamed Abd-Elhameed, Amr Ahmed Elmasry, Ahmed Gamal Atta   +3 more
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On a Novel Approximate Solution to the Inhomogeneous Euler–Bernoulli Equation with an Application to Aeroelastics [PDF]

Aerospace, 2021
This paper focuses on the development of an explicit finite difference numerical method for approximating the solution of the inhomogeneous fourth-order Euler–Bernoulli beam bending equation with velocity-dependent damping and second moment of area, mass
Dominique Fleischmann, László Könözsy   +1 more
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Euler–Bernoulli beams from a symmetry standpoint-characterization of equivalent equations

Journal of Mathematical Analysis and Applications, 2008
We completely solve the equivalence problem for Euler-Bernoulli equation using Lie symmetry analysis. We show that the quotient of the symmetry Lie algebra of the Bernoulli equation by the infinite-dimensional Lie algebra spanned by solution symmetries is a representation of one of the following Lie algebras: $2A_1$, $A_1\oplus A_2$, $3A_1$, or $A_{3,3}
Wafo Soh, Célestin
openaire   +4 more sources