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1986
The free undamped infinitesimal transverse vibrations, of frequency ω*, of a thin straight beam of length l shown in Figure 10.1.1 are governed by the Euler-Bernoulli equation $$\frac{{{d^2}}}{{d{x^2}}}\left( {EI(x)\frac{{{d^2}u(x)}}{{d{x^2}}}} \right) = A(x)\rho {\omega ^{ * 2}}u(x),0\underline < x\underline < \ell .$$ (10.1.1) .
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The free undamped infinitesimal transverse vibrations, of frequency ω*, of a thin straight beam of length l shown in Figure 10.1.1 are governed by the Euler-Bernoulli equation $$\frac{{{d^2}}}{{d{x^2}}}\left( {EI(x)\frac{{{d^2}u(x)}}{{d{x^2}}}} \right) = A(x)\rho {\omega ^{ * 2}}u(x),0\underline < x\underline < \ell .$$ (10.1.1) .
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Chaotic dynamics of flexible Euler-Bernoulli beams
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2013Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the ...
Awrejcewicz, J. +5 more
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2021
This chapter presents the analytical description of thin, or so-called shear-rigid, beam members according to the Euler–Bernoulli theory. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equations, which describe the physical ...
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This chapter presents the analytical description of thin, or so-called shear-rigid, beam members according to the Euler–Bernoulli theory. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equations, which describe the physical ...
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Control of a viscoelastic translational Euler–Bernoulli beam
Mathematical Methods in the Applied Sciences, 2016In this paper, we study a cantilevered Euler–Bernoulli beam fixed to a base in a translational motion at one end and to a tip mass at its free end. The beam is subject to undesirable vibrations, and it is made of a viscoelastic material that permits a certain weak damping.
Berkani, Amirouche +2 more
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Euler–Bernoulli beams with multiple singularities in the flexural stiffness
European Journal of Mechanics - A/Solids, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
BIONDI B, CADDEMI, Salvatore
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Fragile points method for Euler–Bernoulli beams
European Journal of Mechanics - A/SolidszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abinash Malla, Sundararajan Natarajan
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Active and passive Damping of Euler-Bernoulli Beams and Their Interactions
Journal of Dynamic Systems, Measurement, and Control, 1992Active and Passive damping of Euler-Bernoulli beams and their interactions have been studied using the beam’s exact transfer function model without mode truncation or finite element or finite difference approximation. The combination of viscous and Voigt damping is shown to map the open-loop poles and zeros from the imaginary axis in the undamped case ...
Pang, S. T., Tsao, T.-C., Bergman, L. A.
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Stabilization of a viscoelastic rotating Euler‐Bernoulli beam
Mathematical Methods in the Applied Sciences, 2018In this paper, we consider a rotating Euler‐Bernoulli beam. The beam is made of a viscoelastic material, and it is subject to undesirable vibrations. Under a suitable control torque applied at the motor, we prove the arbitrary stabilization of the system for a large class of relaxation functions by using the multiplier method and some ideas introduced ...
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A Local/Nonlocal Elasticity Model for the Euler-Bernoulli Beam
Civil-Comp Proceedings, 2015In this paper a local/nonlocal elasticity model is presented for the statics of the Euler-Bernoulli beam. An integral form of the local/nonlocal elastic constitutive equations for axial deformation and bending are considered with a particular choice of the attenuation function.
FAILLA, ISABELLA +2 more
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Stabilization of Euler- Bernoulli Beam by A Boundary Control
Results in Mathematics, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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