Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics

Śniady Paweł; Katarzyna Misiurek; Olga Szyłko-Bigus; Idzikowski Rafał

doi:10.2478/sgem-2019-0049

.blurhash-client-img { display: none !important; }

Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics

Studia Geotechnica et Mechanica

Volume 42 (2020): Issue 4 (December 2020)

By: Śniady Paweł, Katarzyna Misiurek, Olga Szyłko-Bigus and Idzikowski Rafał

Open Access

|Jun 2020

Figures & Tables

Stress gradient model. Displacement and bending moment of the beam for T = 0.5, *η_g* = 0.01.

Strain gradient model. Displacement and bending moment of the beam for T = 0.5, *η_g* = 0.01.

Stress gradient model. Displacement and bending moment of the beam for T = 0.5, *η_g* = 0.05.

Stress gradient model. Displacement and bending moment of the beam for T = 0.5, *η_g* = 0.10.

Strain gradient model. Displacement and bending moment of the beam for T = 0.5, *η_g* = 0.10.

Stress gradient model. Vibrations of the beam in the middle cross section if *η_g* = 0.01.

Strain gradient model. Vibrations of the beam in the middle cross section if *η_g* = 0.01.

Stress gradient model. Vibrations of the beam in the middle cross-section if *η_g* = 0.05.

Strain gradient model. Vibrations of the beam in the middle cross-section if *η_g* = 0.05.

Stress gradient model. Vibrations of the beam in the middle cross section if *η_g* = 0.10.

Strain gradient model. Vibrations of the beam in the middle cross-section if *η_g* = 0.10.

Table 1

Relation for nonlocal material properties m_e, m_s and the ratio of the critical force velocity to wave velocity.

μ_e = μ_s	$η_{e, cr} = \frac{v_{e, cr}}{v_{g}}$	$η_{s, cr} = \frac{v_{s, cr}}{v_{g}}$
0.2	0.0886	0.124
0.4	0.0652	0.168
0.6	0.0489	0.224

References

Authors

Metrics

Articles in this issue

DOI: https://doi.org/10.2478/sgem-2019-0049 | Journal eISSN: 2083-831X (formerly 0137-124X) | Journal ISSN: 0137-6365

Journal RSS Feed

Language: English

Page range: 306 - 318

Submitted on: Jan 14, 2020

Accepted on: Apr 16, 2020

Published on: Jun 29, 2020

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Keywords:

beam,

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2020 Śniady Paweł, Katarzyna Misiurek, Olga Szyłko-Bigus, Idzikowski Rafał, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 42 (2020): Issue 4 (December 2020)

Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics

Figures & Tables

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Table 1

Paradigm

My account