Unsteady vibration model of the euler-bernoulli beam taking into account diffusion

In this paper we study the unsteady vibration problem for the Euler-Bernoulli beam taking mass transfer into account. To formulate the problem, we use the coupled elastic diffusion model for a homogeneous isotropic multicomponent continuum. Equations of motion and mass transfer are written in the va...

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Bibliographic Details
Published in:Journal of physics. Conference series 2019-02, Vol.1158 (4), p.42043
Main Authors: Zemskov, A V, Tarlakovskii, D V
Format: Article
Language:English
Subjects:
Equations of motion
Euler-Bernoulli beams
Fourier series
Laplace transforms
Mass transfer
Vibration
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Summary:In this paper we study the unsteady vibration problem for the Euler-Bernoulli beam taking mass transfer into account. To formulate the problem, we use the coupled elastic diffusion model for a homogeneous isotropic multicomponent continuum. Equations of motion and mass transfer are written in the variational form of the Hamilton functional. Using the necessary condition for the Hamilton functional stationarity, we obtain the unsteady plane bending model for an elastodiffusive beam. To solve this problem, we use the integral Laplace transform with respect to time and expansion in Fourier series with respect to spatial coordinate.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1158/4/042043