Comptes Rendus
no. 9
Asymptotics of natural oscillations of a spatial junction of thin elastic rods
Sergei A. Nazarov1, 2, 3; Andrey S. Slutskij1, 3
1 Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia
2 Saint Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, 195251, Saint Petersburg, Russia
3 Institute of Problems of Mechanical Engineering RAS, V.O., Bol'shoi pr., 61, 199178, Saint Petersburg, Russia
Comptes Rendus. Mécanique, Volume 344 (2016) no. 9, pp. 684-688.

A one-dimensional model of an elastic junction that contains hard- and readily-movable thin rods is derived, and asymptotic formulas for eigenvalues with rigorous estimates for remainders are given. In addition to vector functions satisfying classical ordinary differential equations, the model involves algebraic unknowns and algebraic relations corresponding to the longitudinal rigid motion of readily-movable rods.

Nous obtenons un modèle 1D d'une jonction élastique qui contient des barres dures fines facilement déplaçables, et nous donnons un développement asymptotique des valeurs propres justifié par des estimations d'erreur rigoureuses. En plus de fonctions vectorielles satisfaisant des équations différentielles ordinaires, le modèle met en jeu des inconnues et des relations algébriques correspondant au mouvement rigide longitudinal des barres.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2016.04.001
Keywords: Elastic junction of thin rods, Hard- and readily-movable rods, Natural oscillations, Asymptotics, Dimension reductions
Mots-clés : Jonction élastique de barres fines, Barres dures déplaçables, Oscillations libres, Analyse asymptotique, Réduction de dimension

Sergei A. Nazarov 1, 2, 3; Andrey S. Slutskij 1, 3

1 Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia
2 Saint Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, 195251, Saint Petersburg, Russia
3 Institute of Problems of Mechanical Engineering RAS, V.O., Bol'shoi pr., 61, 199178, Saint Petersburg, Russia 
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Sergei A. Nazarov; Andrey S. Slutskij. Asymptotics of natural oscillations of a spatial junction of thin elastic rods. Comptes Rendus. Mécanique, Volume 344 (2016) no. 9, pp. 684-688. doi : 10.1016/j.crme.2016.04.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.04.001/

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☆ The work was supported by St.-Petersburg University, grant 0.38.237.2014, and Russian Foundation of Basic Research, grant 15-01-02175.

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