 Phantom solutions analysis through transient dynamics TÉMAKIÍRÁS Intézmény: Budapesti Műszaki és Gazdaságtudományi Egyetem gépészeti tudományok Pattantyús-Ábrahám Géza Gépészeti Tudományok Doktori Iskola témavezető: Habib Giuseppe helyszín (magyar oldal): BME Department of Applied Mechanics helyszín rövidítés: MM A kutatási téma leírása: 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. The analysis of transient dynamics can be very informative in this respect. b.) Aim of research: This research aims at defining a new procedure for identifying dangerous regions of the parameter space through the analysis of transient dynamics. In particular, the research will focus on the systematic identification of phantom solutions, precursors of bi-stable regions. c.) Tasks, main items, necessary time: - study existing methods for the analysis of transient dynamics. - propose more than one method for identifying slower regions of the phase space. The methods should exploit coordinate transformation, statistical quantities, frequency and amplitude analysis, clusterization of the phase space. - apply the procedures to numerical systems presenting a stable equilibrium point coexisting with an unstable limit cycle, such as wheel shimmy, turning machining, flutter instability. - extend the methods to large dimensional systems and combine them with a nonlinear model reduction technique. - test the method experimentally on one of the systems 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: one or more new methodologies 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, vol. 111, no. 22, pp. 20579-20596, 2023. előírt nyelvtudás: English felvehető hallgatók száma: 1 Jelentkezési határidő: 2024-10-15 |