Thesis supervisor: Giuseppe Habib
Location of studies (in Hungarian): Department of Applied Mechanics Abbreviation of location of studies: MM
Description of the research topic:
a.) Preliminaries:
One of the main problems caused by nonlinearities in mechanical systems is that stability analysis is not a sufficient tool for assessing the safety of a device. In particular, the analysis based on a linearized system, typical in engineering practice, might overlook dangerous solutions of the dynamical system at hand co-existing with the desired one, which might be triggered if the system undergoes sufficiently large perturbations.
b.) Aim of research:
This research aim at defining a new procedure for assessing the robustness against external perturbation of stable solutions of a dynamical system. The procedure will be based on time simulations or experiments
c.) Tasks, main items, necessary time:
- study existing methods for basins of attraction estimation
- study existing robustness measures
- develop an algorithm for robustness assessment exploiting trajectories in the phase space of mechanical systems
- apply the procedure to archetypal examples of multi-stable systems, such as the Helmholtz, the Duffing, and the rigid block oscillators
- choosing one of the multi-stable systems presented at the previous point, implement the developed algorithm experimentally for robustness assessment
Estimated necessary time: 3 years
d.) Required equipment:
- one laptop equipped with a relatively fast processor
- mechanical components, such as spring, plates, and beams, are necessary for mechanical tests
e.) Expected scientific results:
The research outcome will mainly constitute an easy-to-use algorithm for robustness assessment, implementable in various engineering fields. A tool so far missing.
f.) References:
[1] S. Lenci and G. Rega, Global Nonlinear Dynamics for Engineering Design and System Safety. Springer, 2019.
[2] G. Habib, “Dynamical integrity assessment of stable equilibria: a new rapid iterative procedure,” Nonlinear Dynamics, vol. 106, no. 3, pp. 2073–2096, 2021.
[3] C. S. Hsu, Cell-to-cell mapping: a method of global analysis for nonlinear systems, vol. 64. Springer Science & Business Media, 2013.
Required language skills: English Number of students who can be accepted: 1
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