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An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation

1
Research Institute of Mechanics, Lomonosov Moscow State University, 119192 Moscow, Russia
2
Moscow Aviation Institute (National Research University), 125993 Moscow, Russia
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(1), 23; https://doi.org/10.3390/mca24010023
Received: 29 December 2018 / Revised: 30 January 2019 / Accepted: 30 January 2019 / Published: 6 February 2019
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
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Abstract

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. View Full-Text
Keywords: elastic diffusion; coupled problem; unsteady problem; Green’s function; integral transformation; multicomponent continuum; Euler–Bernoulli beam elastic diffusion; coupled problem; unsteady problem; Green’s function; integral transformation; multicomponent continuum; Euler–Bernoulli beam
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Tarlakovskii, D.; Zemskov, A. An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation. Math. Comput. Appl. 2019, 24, 23.

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