Milling dynamic model based on rotatory Euler–Bernoulli beam model under distributed load

2020 ◽  
Vol 83 ◽  
pp. 266-283 ◽  
Author(s):  
Qi Yao ◽  
Ming Luo ◽  
Dinghua Zhang
Keyword(s):  
Dynamic Model ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Model Based ◽  
Distributed Load ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

scholarly journals Numerical Solution of Bending of the Beam with Given Friction

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 898
Author(s):  
Michaela Bobková ◽  
Lukáš Pospíšil
Keyword(s):  
Sliding Friction ◽  
Quadratic Function ◽  
Building Construction ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Sustainable Building ◽  
Construction Design ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Fixed Beam

We are interested in a contact problem for a thin fixed beam with an internal point obstacle with possible rotation and shift depending on a given swivel and sliding friction. This problem belongs to the most basic practical problems in, for instance, the contact mechanics in the sustainable building construction design. The analysis and the practical solution plays a crucial role in the process and cannot be ignored. In this paper, we consider the classical Euler–Bernoulli beam model, which we formulate, analyze, and numerically solve. The objective function of the corresponding optimization problem for finding the coefficients in the finite element basis combines a quadratic function and an additional non-differentiable part with absolute values representing the influence of considered friction. We present two basic algorithms for the solution: the regularized primal solution, where the non-differentiable part is approximated, and the dual formulation. We discuss the disadvantages of the methods on the solution of the academic benchmarks.

scholarly journals Critical Velocity of High-Performance Yarn Transversely Impacted by Razor Blade

Fibers ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 95 ◽  
Author(s):  
Boon Lim ◽  
Jou-Mei Chu ◽  
Benjamin Claus ◽  
Yizhou Nie ◽  
Wayne Chen
Keyword(s):  
Critical Velocity ◽  
High Speed ◽  
High Performance ◽  
Hertzian Contact ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Razor Blade ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Hertzian Contact Model

A ballistic parameter that influences the ballistic performances of a high-performance yarn is the critical velocity. The critical velocity is defined as the projectile striking velocity that causes instantaneous rupture of the yarn upon impact. In this study, we performed ballistic experiments to determine the critical velocity of a Twaron® yarn transversely impacted by a razor blade. A high-speed camera was integrated into the experimental apparatus to capture the in-situ deformation of the yarn. The experimental critical velocity demonstrated a reduction compared to the critical velocity predicted by the classical theory. The high-speed images revealed the yarn specimen failed from the projectile side toward the free end when impacted by the razor blade. To improve the prediction capability, the Euler–Bernoulli beam and Hertzian contact models were used to predict the critical velocity. For the Euler–Bernoulli beam model, the critical velocity was obtained by assuming the specimen ruptured instantaneously when the maximum flexural strain reached the ultimate tensile strain of the yarn upon impact. On the other hand, for the Hertzian contact model, the yarn was assumed to fail when the indentation depth was equivalent to the diameter of the yarn. The errors between the average critical velocities determined from experiments and the predicted critical velocities were around 19% and 48% for the Euler–Bernoulli beam model and Hertzian contact model, respectively.

Noether symmetries and exact solutions of an Euler–Bernoulli beam model

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640011 ◽  
Author(s):  
Aeeman Fatima ◽  
Fazal M. Mahomed ◽  
Chaudry Masood Khalique
Keyword(s):  
Exact Solutions ◽  
Order Equation ◽  
Beam Equation ◽  
Beam Model ◽  
Noether Symmetries ◽  
Bernoulli Beam ◽  
Lagrange Equations ◽  
New Exact Solutions ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

In this paper, a Noether symmetry analysis is carried out for an Euler–Bernoulli beam equation via the standard Lagrangian of its reduced scalar second-order equation which arises from the standard Lagrangian of the fourth-order beam equation via its Noether integrals. The Noether symmetries corresponding to the reduced equation is shown to be the inherited Noether symmetries of the standard Lagrangian of the beam equation. The corresponding Noether integrals of the reduced Euler–Lagrange equations are deduced which remarkably allows for three families of new exact solutions of the static beam equation. These are shown to contain all the previous solutions obtained from the standard Lie analysis and more.

On the forced vibration of carbon nanotubes via a non-local Euler—Bernoulli beam model

2010 ◽  
Vol 224 (2) ◽  
pp. 497-503 ◽  
Author(s):  
P Karaoglu ◽  
M Aydogdu
Keyword(s):  
Carbon Nanotubes ◽  
Forced Vibration ◽  
Beam Theory ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Resonance Frequencies ◽  
Non Local ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Walled Cnts

This article studies the forced vibration of the carbon nanotubes (CNTs) using the local and the non-local Euler—Bernoulli beam theory. Amplitude ratios for the local and the non-local Euler—Bernoulli beam models are given for single- and double-walled CNTs. It is found that the non-local models give higher amplitudes when compared with the local Euler—Bernoulli beam models. The non-local Euler—Bernoulli beam model predicts lower resonance frequencies.

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