| Issue |
Math. Model. Nat. Phenom.
Volume 17, 2022
Recent Trends in Hyperbolic Equations in Physical Systems
|
|
|---|---|---|
| Article Number | 24 | |
| Number of page(s) | 19 | |
| DOI | https://doi.org/10.1051/mmnp/2022028 | |
| Published online | 01 August 2022 | |
Nonlocal longitudinal vibration in a nanorod, a system theoretic analysis
1
Department of Applied Mathematics, School of Mathematics and Computer Science, Damghan University, Damghan, P.O. Box 36715-364, Iran
2
Department of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, 7500 AE Enschede, The Netherlands
3
Faculty of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
* Corresponding author: heidari@du.ac.ir
Received:
17
December
2021
Accepted:
27
June
2022
Analysis of longitudinal vibration in a nanorod is an important subject in science and engineering due to its vast application in nanotechnology. This paper introduces a port-Hamiltonian formulation for the longitudinal vibrations in a nanorod, which shows that this model is essentially hyperbolic. Furthermore, it investigates the spectral properties of the associated system operator. Standard distributed control and feedback are shown not to be controllable nor stabilizing.
Mathematics Subject Classification: 74H45 / 47D03 / 74-10 / 93C20
Key words: Port-Hamiltonian / Riesz basis / contraction semigroup / nanotubes / controllability / stabilisability
© The authors. Published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.