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A family of isospectral Euler–Bernoulli beams
Inverse Problems, 2010In this paper we consider the class of Euler–Bernoulli beams such that the product between the bending stiffness and the linear mass density is constant. Under the assumption that the end conditions are any combination of pinned and sliding, we obtain closed-form expressions for beams isospectral to a given one.
GLADWELL GML, MORASSI, Antonino
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Approximate Solutions to Euler–Bernoulli Beam Type Equation
Mediterranean Journal of Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Md. Maqbul, Nishi Gupta
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Dynamic analogy between Timoshenko and Euler–Bernoulli beams
Acta Mechanica, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
De Rosa M. A. +4 more
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2019
This chapter covers the continuum mechanical description of thin beam members. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law and the equilibrium equation, the partial differential equation, which describes the physical problem, is derived.
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This chapter covers the continuum mechanical description of thin beam members. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law and the equilibrium equation, the partial differential equation, which describes the physical problem, is derived.
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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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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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Vibrations of Cracked Euler-Bernoulli Beams
2014In this Chapter, the Haar wavelet method is applied for analysing bending and vibrations of elastic Euler-Bernoulli beams.
Ülo Lepik, Helle Hein
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Viscoelastically supported Euler-Bernoulli beam
2001A field of application for the convolution quadrature method are time dependent integral equations. Here, the integral equation for a transient excited viscoelastically supported Euler-Bernoulli beam will be deduced and solved with the convolution quadrature method. A direct evaluation in time domain is only possible without the viscoelastic foundation,
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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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On the Curvature of an Euler–Bernoulli Beam
International Journal of Mechanical Engineering Education, 2003This paper deals with different approaches to describing the relationship between the bending moment and curvature of a Euler—Bernoulli beam undergoing a large deformation, from a tutorial point of view. First, the concepts of the mathematical and physical curvature are presented in detail.
KOPMAZ, OSMAN, GÜNDOĞDU, ÖMER
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