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Title Approximate symmetries and conservation laws for mechanical systems described by mixed derivative perturbed PDEs
Authors Shamaoon, A.
Agarwal, P.
Cesarano, C.
Jain, S.
ORCID
Keywords beams oscillations
traveling-wave reduction
conserved vectors
Noether approach
Type Article
Date of Issue 2023
URI https://essuir.sumdu.edu.ua/handle/123456789/93338
Publisher Sumy State University
License Creative Commons Attribution - NonCommercial 4.0 International
Citation Shamaoon A., Agarwal P., Cesarano C., Jain S. (2023). Approximate symmetries and conservation laws for mechanical systems described by mixed derivative perturbed PDEs. Journal of Engineering Sciences (Ukraine), Vol. 10(2), pp. E8–E15. DOI: 10.21272/jes.2023.10(2).e2
Abstract This article focuses on developing and applying approximation techniques to derive conservation laws for the Timoshenko–Prescott mixed derivatives perturbed partial differential equations (PDEs). Central to our approach is employing approximate Noether-type symmetry operators linked to a conventional Lagrangian one. Within this framework, this paper highlights the creation of approximately conserved vectors for PDEs with mixed derivatives. A crucial observation is that the integration of these vectors resulted in the emergence of additional terms. These terms hinder the establishment of the conservation law, indicating a potential flaw in the initial approach. In response to this challenge, we embarked on the rectification process. By integrating these additional terms into our model, we could modify the conserved vectors, deriving new modified conserved vectors. Remarkably, these modified vectors successfully satisfy the conservation law. Our findings not only shed light on the intricate dynamics of fourth-order mechanical systems but also pave the way for refined analytical approaches to address similar challenges in PDE-driven systems.
Appears in Collections: Journal of Engineering Sciences / Журнал інженерних наук

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