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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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Euler–Bernoulli Beams and Frames
2016This chapter starts with the analytical description of 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.
Andreas Öchsner, Marco Öchsner
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Exact solutions of Euler–Bernoulli beams
Modern Physics Letters B, 2023In numerous real-world applications, transverse vibrations of beams are nonlinear in nature. It is a task to solve nonlinear beam systems due to their substantial dependence on the 4 variables of the system and the boundary conditions. To comprehend the nonlinear vibration characteristics, it is essential to do a precise parametric analysis.
Jamil Abbas Haider +5 more
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A tracking controller for the Euler-Bernoulli beam
Proceedings., IEEE International Conference on Robotics and Automation, 2002A controller for the Euler-Bernoulli beam is presented with a view to its application on a flexible link robot. It is shown that the controller guarantees asymptotic trajectory tracking for a particular class of initial conditions, requires limited feedback information, and is simple to design.
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2009
A beam is defined as a structure having one of its dimensions much larger than the other two. The axis of the beam is defined along that longer dimension, and a crosssection normal to this axis is assumed to smoothly vary along the span or length of the beam. Civil engineering structures often consist of an assembly or grid of beams with cross-sections
Bauchau, Olivier, Craig, J.I.
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A beam is defined as a structure having one of its dimensions much larger than the other two. The axis of the beam is defined along that longer dimension, and a crosssection normal to this axis is assumed to smoothly vary along the span or length of the beam. Civil engineering structures often consist of an assembly or grid of beams with cross-sections
Bauchau, Olivier, Craig, J.I.
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Observer for Euler-Bernoulli beam with hydraulic drive
Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), 2002It is shown how to extend passivity and contraction results for flexible mechanisms with electrical drives to systems with hydraulic drives.
Olav Egeland +2 more
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Motion planning for a damped euler-bernoulli beam
49th IEEE Conference on Decision and Control (CDC), 2010The motion planning problem is considered for a Euler-Bernoulli beam with viscous damping. For its solution, a systematic spectral approach is proposed, which is based on the Riesz spectral properties of the system operator. This enables to analyze both boundary and in-domain control in a common framework.
Thomas Meurer +2 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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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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