Contributions to the method development for the vibration analysis of structures with contact nonlinearities
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Beschreibung
Despite methodological advances, vibration prediction of systems with contact nonlinearities remains computationally intensive. This thesis aims to enhance current practices, which typically rely on Harmonic Balance method with Alternating-Frequency-Time scheme and predictor-corrector path continuation. The focus is on systems with strong nonlinear boundary forces, such as frictional and unilateral contact.
First, the combination of classical Harmonic Balance method with the Asymptotic Numerical Method is evaluated. While effective for smooth nonlinearities, it underperforms compared to the established predictor-corrector approach in contact problems. Second, a novel Chebyshev-based method for the efficient evaluation of Floquet stability is proposed, offering significant computational savings for smooth systems but its benefit diminishes for systems involving contact. Third, the systematic numerical evaluation of Urabe’s a posteriori error estimator is explored, enabling adaptive Harmonic Balance analysis, but involving prohibitive computational cost for systems involving contact. Finally, the thesis provides one of the first successful analytical bifurcation analysis involving a Jenkins element, revealing how modal interactions can undermine the stabilizing effect of friction damping in flutter phenomena.
Autor*in
Lukas Woiwode
Themen in »Contributions to the method development for the vibration analysis of structures with contact nonlinearities«
Nonlinear dynamics Bifurcation analysis Contact nonlinearity