Summary
The study of the elastic lamina by Euler is compound of a static part and of a part dedicated to the study of the oscillations of the rod. This study plays an important role in the elaboration of the concepts of shear and stress and are with them in the center of the preoccupations of engineers. The brave attempt, unfortunately wrong, due to Jacob II Bernoulli to generalise to two dimensions the theory of the oscillations of the elastic rod underlines the difficulties.
Résumé
L’étude de la lame élastique par Euler comprend une partie statique et une partie consacrée à l’étude des oscillations de la lame. Cette étude joue un rôle important dans l’élaboration des concepts de tension et de cisaillement et sont avec celles-ci au centre des préoccupations des ingénieurs. La tentative courageuse mais malheureusement entachée d’erreur, due à Jacob II Bernoulli de généraliser à deux dimensions l’étude du mouvement d’oscillation de la lame élastique nous en montre les difficultés.
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References
G. Galilei, Discorsi et Dimostrazioni matematiche intorno a due nuove scienze attenenti alla Meccanica e i movimenti locali, Leiden, 1638.
L. Euler, Opera Omnia, Vol XI, Pt. 2.
L. Euler, Methodus Inveniendi lineas curvas maximi minimive proprie tate gaudentes, Lausanne, 1744.
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© 1995 Birkh¤user Verlag
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Mathúna, D.Ó. (1995). Jacob II Bernoulli and the Problem of the Vibrating Plate. In: Grave, P.Rd., Benvenuto, E. (eds) Entre Mécanique et Architecture / Between Mechanics and Architecture. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9072-4_10
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DOI: https://doi.org/10.1007/978-3-0348-9072-4_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9894-2
Online ISBN: 978-3-0348-9072-4
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