Nonlocal longitudinal vibration in a nanorod, a system theoretic analysis

Hanif Heidari¹ ; Hans Zwart^2, 3

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

Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 24.

Résumé

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.

Détail

DOI : 10.1051/mmnp/2022028

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