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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 9, Pages 84–89 (Mi ivm9156)  
This article is cited in 5 scientific papers (total in 5 papers)

Brief communications

Refined geometrically nonlinear equations of motion for elongated rod-type plate

A. M. Kamalutdinova, V. N. Paimushinb

a Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
b Kazan National Research Technical University, 10 K. Marks str., Kazan, 420111 Russia
Full-text PDF (148 kB) Citations (5)
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Abstract: We derive new refined geometrically nonlinear equations of motion for elongated rod-type plates. They are based on the proposed earlier relationships of geometrically nonlinear theory of elasticity in the case of small deformations and refined S. P. Timoshenko's shear model. These equations allow to describe the high-frequency torsional oscillation of elongated rod-type plate formed in them when plate performs low-frequency flexural vibrations. By limit transition to the classical model of rod theory we carry out transformation of derived equations to simplified system of equations of lower degree.
Keywords: elongated rod-type plate, equations of elasticity theory, kinematic relationships in the quadratic approximation, Timoshenko's model, geometric nonlinearity, equations of motion, classical model, optimization, simplified equations of motion.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Russian Science Foundation 14-19-00667
Received: 01.02.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 9, Pages 74–78
DOI: https://doi.org/10.3103/S1066369X16090103
Bibliographic databases:
Document Type: Article
UDC: 531.121
Language: Russian
Citation: A. M. Kamalutdinov, V. N. Paimushin, “Refined geometrically nonlinear equations of motion for elongated rod-type plate”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 9, 84–89; Russian Math. (Iz. VUZ), 60:9 (2016), 74–78
Citation in format AMSBIB
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\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\pages 84--89
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\issue 9
\pages 74--78
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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