Modeling of the quasi-periodic galloping response type under combined harmonic and random excitation

0509003 - ÚTAM 2022 eng A - Abstract
Náprstek, Jiří - Fischer, Cyril - Pospíšil, Stanislav
Modeling of the quasi-periodic galloping response type under combined harmonic and random excitation.
The Sixteenth International Conference on Civil, Structural & Environmental Engineering Computing. [S.l.]: Oxfordabstracts.com, 2019 - (Topping, B.)
[International Conference on Civil, Structural & Environmental Engineering Computing. CIVIL COMP /16./. 16.09.2019-19.09.2019, Riva del Garda]
Institutional support: RVO:68378297
Keywords : Van der Pol equation * lock-in regime * combined harmonic and random excitation * quasi-periodic response * detuning in the resonance zone
OECD category: Civil engineering

The paper is motivated by wind tunnel experiments investigating SDOF model of a rope with ice accretion. The response is a combination of self-excited and forced vibration in several zones of detuning, which results in quasi-periodic effects. The random component of the excitation significantly influences all regimes of the response. Comparison of experimental results and those following from the new theoretical model shows a good applicability of the van der Pol type modeling of effects observed.The amplitudes of the response can form closed hysteresis loops or unstable zones if the wind velocity is swept up/down. Right side consists of deterministic and random parts. The vortex shedding frequency is synchronized nearly with the eigen frequency. The detuning can be influenced by means of roughness of the surface, damping ratio, etc. Two components of the total response manifest in the resonance zone: (i) self-excited vibration stabilized on a limit cycle; (ii) forced vibration due to the harmonic part of the excitation on the right side. The resulting response exhibits quasi-periodic beatings. The input process can be considered of the Markov type and, therefore, the relevant Fokker-Planck Equation for the cross-probability density function for amplitudes ac, as can be written and investigated. The FPE should be kept in evolutionary form to enable to investigate the quasi-periodic type of the system response in the resonance zone. The harmonic balance procedure can be employed outside the resonance zone due to fact that the stationary state of the response PDF exists in this frequency domain.
Permanent Link: http://hdl.handle.net/11104/0327471