Applications of Some Extremal and Variational Problems to the Study of Vibrations in Mechanical Systems

DOI

10.2991/978-94-6463-152-4_11How to use a DOI?

Keywords

Extremal; Variational problems; Vibrations; Mechanical systems

Abstract

The object of the present study is the mathematical side of extremi-related problems. We have studied certain applications of the variational calculus in the domain of vibrations existing in mechanical systems. The most frequently encountered problem in the matter of vibrations is the one of determining the naturally occurring frequencies of a vibrating system. In the practice of engineering, it is the lowest frequency also known as the fundamental one which does present the highest interest. In order to determine the natural frequencies, the usually employed strategy is a combination between Rayleigh’s energetical method and the Ritz procedure. Briefly described it does consist in applying a form of vibration or a configuration which should essentially be the intrinsic one of the concerned systems at the moment when it would be situated in the position reflecting the largest possible extent of its translation movement which ought to correspond to its fundamental functioning. We have as well pointed out the advantage which could be taken from applying the integer transformations in the resolution of some extremi-related problems since this choice would render them algebraically shaped and thereby would considerably simplify them.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Valeriu Ionica
AU  - Mihaela Bogdan
AU  - Leonard Marius Ciurezu-Gherghe
AU  - Adrian Bogdan
AU  - Ionut Geonea
PY  - 2023
DA  - 2023/05/30
TI  - Applications of Some Extremal and Variational Problems to the Study of Vibrations in Mechanical Systems
BT  - Proceedings of the International Conference of Mechanical Engineering (ICOME-2022)
PB  - Atlantis Press
SP  - 96
EP  - 106
SN  - 2589-4943
UR  - https://doi.org/10.2991/978-94-6463-152-4_11
DO  - 10.2991/978-94-6463-152-4_11
ID  - Ionica2023
ER  -