scholarly journals Euler-Bernoulli cantilever beam bending considering the inner diffusion flows finite propagation speed

2020 ◽  
pp. 107-114
Author(s):  
Андрей Владимирович Земсков ◽  
Георгий Михайлович Файкин
Keyword(s):  
Mass Transfer ◽  
Propagation Speed ◽  
Bernoulli Beam ◽  
Elastic Diffusion ◽  
Multicomponent Media ◽  
Equivalent Boundary ◽  
Beam Bending ◽  
Finite Propagation Speed ◽  
Euler Bernoulli Beam ◽  
Diffusion Flows

Исследуются нестационарные колебания балки Эйлера-Бернулли с учетом массопереноса. Используется модель упругой диффузии для многокомпонентных сред. Для получения решения задачи используются вариационный принцип Даламбера и метод эквивалентный граничных условий. Unsteady vibrations of the Euler-Bernoulli beam are studied taking into account mass transfer. The model of elastic diffusion for multicomponent media is used. To obtain a solution to the problem, the d’Alembert variational principle and the equivalent boundary conditions method are used.

scholarly journals An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation

2019 ◽  
Vol 24 (1) ◽  
pp. 23 ◽  
Author(s):  
Dmitry Tarlakovskii ◽  
Andrei Zemskov
Keyword(s):  
Fourier Series ◽  
Variational Principle ◽  
Laplace Transform ◽  
Diffusion Flux ◽  
Fourier Series Expansion ◽  
Bernoulli Beam ◽  
Elastic Diffusion ◽  
The Laplace Transform ◽  
Flux Relaxation ◽  
Euler Bernoulli Beam

This article considers an unsteady elastic diffusion model of Euler–Bernoulli beam oscillations in the presence of diffusion flux relaxation. We used the model of coupled elastic diffusion for a homogeneous orthotropic multicomponent continuum to formulate the problem. A model of unsteady bending for the elastic diffusive Euler–Bernoulli beam was obtained using Hamilton’s variational principle. The Laplace transform on time and the Fourier series expansion by the spatial coordinate were used to solve the obtained problem.

Position of Shelf Supports

1998 ◽  
Vol 26 (4) ◽  
pp. 338-344
Author(s):  
J. P. Ward
Keyword(s):  
Differential Equation ◽  
Strain Energy ◽  
Bernoulli Beam ◽  
Simple Support ◽  
Beam Bending ◽  
Simple Supports ◽  
Euler Bernoulli Beam

Using the Euler–Bernoulli beam-bending differential equation we analyse the solution for a shelf deformed under gravity in two situations: (a) simple supports positioned at x = β and x = L – β and (b) Cantilever at one end with a simple support at x = β. We ask where the best position for the supports should be. A number of alternative positions are suggested though the eventual choice of support position is chosen to be that which minimizes the shelf's strain energy.

LMI-based hybrid temporal-spatial differential control design for a class of Euler-Bernoulli beam system

2021 ◽  
pp. 095440622110036
Author(s):  
Jiaqi Zhong ◽  
Xiaolei Chen ◽  
Yupeng Yuan ◽  
Jiajia Tan
Keyword(s):  
Vibration Suppression ◽  
Direct Method ◽  
Recursive Algorithm ◽  
Linear Matrix ◽  
Bernoulli Beam ◽  
Hybrid Controller ◽  
Beam System ◽  
Active Vibration ◽  
Differential Control ◽  
Euler Bernoulli Beam

This paper addresses the problem of active vibration suppression for a class of Euler-Bernoulli beam system. The objective of this paper is to design a hybrid temporal-spatial differential controller, which is involved with the in-domain and boundary actuators, such that the closed-loop system is stable. The Lyapunov’s direct method is employed to derive the sufficient condition, which not only can guarantee the stabilization of system, but also can improve the spatial cooperation of actuators. In the framework of the linear matrix inequalities (LMIs) technology, the gain matrices of hybrid controller can obtained by developing a recursive algorithm. Finally, the effectiveness of the proposed methodology is demonstrated by applying a numerical simulation.

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