Session: MSNDC-04-02 Nonlinear Dynamics of Structures

Paper Number: 97895

97895 - Stability Analysis of Stable Branches for a Stochastically Excited One Degree-of-Freedom System With Qubic Geometric Nonlinearity 

The study here targets improving and extending the existing stochastic bifurcation analysis methodologies. A one degree of freedom mechanical system with geometric nonlinearity is forced harmonically with the addition of stochastic excitation. Combining the commonly used pseudo-arc-length method with a Markov model, it is possible to map out the bifurcation branches and then transform the deterministic results into the stochastic case. Based on the Markov model, the stability of the periodic orbits can be approximated over time. This way in-operation burst random excitation can be modelled, which could be an ideal arrangement for an industrial measurement methodology characterizing nonlinearity, concentrating on problems originating from machining, energy and avionic industries. The proposed methodology here is based on the distances between the stable and unstable periodic solutions. From these sections, the probability of stability loss can be derived considering the operation time of the structure. In real-world applications, the measurement of unstable periodic orbits can be cumbersome. Hence, the possibility for the future transition of this methodology to measurement applications requires the approximation of the above-mentioned sections. Solutions for this problem are provided in this study, based on the comparison of the maximum forcing amplitudes of the burst excitation that do not lead to stability loss on the lower or upper stable branches.

Presenting Author: Zoltan Gabos Budapest University of Technology and Economics

Presenting Author Biography: Zoltan Gabos is a PhD student at the Department of Applied Mechanics of Budapest University of Technology and Economics. National Conference of Scientific Students' Association winner in the field of manufacturing with his study about an electromechanical tuned mass damper connected to a boring bar. His main research field is identifying and quantifying nonlinearities of mechanical structures related to machining, considering stochastic excitation combined with the conventional harmonic forcing.

Authors:

Zoltan Gabos Budapest University of Technology and Economics
Zoltan Dombovari Budapest University of Technology and Economics