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

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:
Open Access
|Jun 2020

Figures & Tables

Figure 1

Beam under moving force.
Beam under moving force.

Figure 2

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

Figure 3

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

Figure 4

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

Figure 5

Strain gradient model. Displacement and bending moment of the beam for T = 0.5, ηg = 001.
Strain gradient model. Displacement and bending moment of the beam for T = 0.5, ηg = 001.

Figure 6

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

Figure 7

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

Figure 8

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

Figure 9

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

Figure 10

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

Figure 11

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

Figure 12

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

Figure 13

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

Relation for nonlocal material properties me, ms and the ratio of the critical force velocity to wave velocity_

μe = μsηe,cr=ve,crvg\eta _{e,cr} = \frac{{v_{e,cr} }}{{v_g }}ηs,cr=vs,crvg\eta _{s,cr} = \frac{{v_{s,cr} }}{{v_g }}
0.20.08860.124
0.40.06520.168
0.60.04890.224
DOI: https://doi.org/10.2478/sgem-2019-0049 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
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Language: English
Page range: 306 - 318
Submitted on: Jan 14, 2020
Accepted on: Apr 16, 2020
Published on: Jun 29, 2020
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
vibration,
beam,
moving force,
nonlocal elasticity
Related subjects:
Geosciences,
Geosciences, other,
Materials sciences,
Composites,
Porous materials,
Physics,
Mechanics and fluid dynamics

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

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