Numerical approximation of the dissipativity of energy and spectrum for a damped Euler-Bernoulli beam with variable coefficients

Journal of Nonlinear Sciences and Applications Pub Date : 2023-08-18 DOI:10.22436/jnsa.016.03.01

Bomisso Gossrin, Yapi Serge, Alain Joresse, Tour´e Kidj´egbo Augustin

引用次数: 0

Abstract

This article concerns the numerical study of the behaviour of a ﬂexible beam of Euler-Bernoulli to which one adds to its internal composition a damping of the viscous type. This damping naturally exerts a dissipative force (or viscous damping force) on the beam and opposes any deformation, in proportion to the rate of deformation. We are therefore interested in the impact of the damper on the exponential stability of the beam. We develop here a numerical method which faithfully reproduces the theoretical results obtained by several authors. Simulations are provided to illustrate our results.

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变系数阻尼欧拉-伯努利梁能量耗散率和谱的数值近似

本文讨论了在欧拉-伯努利柔性梁的内部结构中加入粘性型阻尼后其性能的数值研究。这种阻尼自然地在梁上施加耗散力(或粘性阻尼力)，并与变形率成比例地反对任何变形。因此，我们感兴趣的是阻尼器对梁的指数稳定性的影响。我们在这里发展了一种数值方法，它忠实地再现了几位作者的理论结果。通过仿真来说明我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.