Thesis supervisor: Giuseppe Habib
Location of studies (in Hungarian): BME 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 identifying unstable solutions based on a system’s transient dynamics.
c.) Tasks, main items, necessary time:
- study existing methods for identifying unstable solutions, either numerically, analytically or experimentally
- develop an algorithm estimating an unstable periodic solution which limit a system robustness, based on
the transient dynamics of converging trajectories
- apply the procedure to numerical systems presenting a stable equilibrium point coexisting with an unstable
limit cycle, such as wheel shimmy, turning machining, flutter instability.
- extend the method to large dimensional systems and combine it with a nonlinear model reduction
technique.
- test the method experimentally on one of the system considered numerically
Estimated necessary time: 3 years
d.) Required equipment:
- one laptop equipped with a relatively fast processor
- towed wheel on a treadmill for shimmy experiments already available in the laboratory of the MM department
e.) Expected scientific results:
a new methodology to extract information of nonlinear dynamical systems from their trajectories in the phase space
f.) References:
[1] J. Lim and B.I. Epureanu, “Forecasting a class of bifurcations: Theory and experiment,” Physical Review E, vol. 8, no. 1, pp. 016203, 2011.
[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] G. Habib, “Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach,” Nonlinear Dynamics, in print.
Required language skills: English Number of students who can be accepted: 1
Deadline for application: 2024-04-23
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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