Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics

<p> A <emph>point mapping </emph>analysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system&#39;s dynamics, and its dependence on system&#39;s parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an &#8220;exact solution&#8221; for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.</p

Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics

A point mapping analysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system's dynamics, and its dependence on system's parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome

FE sensitivity models and descriptions for Tseng et al.

Tsengetal_PLoS-ONE_FE_models.zip: Finite element models of Gray Wolf mandible sensitivity analysis. Data uploaded by Zhijie Jack Tseng, contact: [email protected]. Zipped file contains sensitivity models J20101112TSA01 to J20101215TSA44. Files include finite element mesh (.st7) and model details and result sheets (.xls) for each model. 2011032