Interaction of a self vibrating beam with chaotic external forces

Joël Chaskalovic; J. Ratsaby

doi:10.1016/j.crme.2009.11.001

Interaction of a self vibrating beam with chaotic external forces
[Interaction entre les vibrations d'une poutre et un champ de forces aléatoires]

Présenté par : Jean-Baptiste Leblond

Joël Chaskalovic ^1,² ; J. Ratsaby ³

¹ Mathematics Department, Ariel University Center, 40700 Ariel, Israel
² IJLRA, University Pierre and Marie Curie, 4, place Jussieu, 75252 Paris cedex 05, France
³ Engineering Department, Ariel University Center, 40700 Ariel, Israel

Comptes Rendus. Mécanique, Volume 338 (2010) no. 1, pp. 33-39.

Résumé
Abstract

La mesure de la complexité des systèmes physiques intervient dans de nombreuses applications des sciences de l'ingénieur. Lin [Entropy 10 (1) (2008) 1–5] a montré que la complexité structurelle d'un système est liée aux propriétés ayant trait à ses symétries géométriques ainsi qu'à sa stabilité dans le temps. Le modèle de Ratsaby [Entropy 10 (1) (2008) 6–14] suggère d'évaluer la complexité des systèmes physiques par analogie à la mesure de la complexité des algorithmes. Selon ce modèle, un système physique sollicité par un environnement chaotique réagit comme une entité qui absorbe une partie du caractère aléatoire des sollicitations qui s'exercent sur celui-ci. Cette Note a pour objet de présenter la réponse d'un système vibratoire simple soumis à un champ de forces aléatoires. On montrera principalement que la relation obtenue entre la complexité du système et le caractère aléatoire du champ de déplacements qui en résulte, est analogue à celle qui prévaut pour les règles de sélection des algorithmes informatiques.

Measuring the complexity of physical systems has been traditionally a problem in numerous engineering applications. Lin [Entropy 10 (1) (2008) 1–5] showed that the structural complexity is related to other properties of a solid such as symmetry and its stability over time. In Ratsaby [Entropy 10 (1) (2008) 6–14] a model was introduced which defines the complexity of a solid structure not by a qualitative notion of entropy but by an algorithmic notion of description complexity. According to the model, a dynamic structure in a random surrounding acts as an interfering entity that deforms randomness. In the current Note we report on the results of an empirical study that analyzes the output response of a simulated elastic beam subjected to a field of external random forces input. The relationship between the complexity of the system and the stochasticity of the output is shown to support this model and is a first indication that solids act similar to algorithmic selection rules.

Reçu le : 2009-03-18
Accepté le : 2009-11-10
Publié le : 2010-01-01

DOI : 10.1016/j.crme.2009.11.001

Keywords: Computer science, Structure complexity, Solids, Randomness
Mot clés : Informatique, Complexité structurelle, Solides, Caractère aléatoire

Affiliations des auteurs :

Joël Chaskalovic ^{1, 2} ; J. Ratsaby ³

¹ Mathematics Department, Ariel University Center, 40700 Ariel, Israel
² IJLRA, University Pierre and Marie Curie, 4, place Jussieu, 75252 Paris cedex 05, France
³ Engineering Department, Ariel University Center, 40700 Ariel, Israel

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Joël Chaskalovic; J. Ratsaby. Interaction of a self vibrating beam with chaotic external forces. Comptes Rendus. Mécanique, Volume 338 (2010) no. 1, pp. 33-39. doi : 10.1016/j.crme.2009.11.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.11.001/

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