<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Two models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of strains gradient, were studied and compared. A dynamic response of a finite, simply supported beam under a moving force was evaluated. The force is moving along the beam with a constant velocity. Particular solutions in the form of an infinite series and some solutions in a closed form as well as the numerical results were presented.</p></abstract>

Two models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of strains gradient, were studied and compared. A dynamic response of a finite, simply supported beam under a moving force was evaluated. The force is moving along the beam with a constant velocity. Particular solutions in the form of an infinite series and some solutions in a closed form as well as the numerical results were presented.

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

Faculty of Environmental Engineering and Geodesy

Wroclaw University of Environmental and Life Science

Wroclaw University of Science and Technology

Studia Geotechnica et Mechanica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Two models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity,...

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

Article Category: Research Article

Published Online: Jun 29, 2020

Page range: 306 - 318

Received: Jan 14, 2020

Accepted: Apr 16, 2020

DOI: https://doi.org/10.2478/sgem-2019-0049

Keywords
vibration, beam, moving force, nonlocal elasticity

© 2020 Paweł Śniady et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Article Category: Research Article

Published Online: Jun 29, 2020

Page range: 306 - 318

Received: Jan 14, 2020

Accepted: Apr 16, 2020

DOI: https://doi.org/10.2478/sgem-2019-0049

Keywordsvibration, beam, moving force, nonlocal elasticity

© 2020 Paweł Śniady et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
vibration, beam, moving force, nonlocal elasticity