http://www.msc.univ-paris-diderot.fr/~phyexp/uploads/EolienneFlexible/EolienneStateArt.pdf

State of the art in wind turbine aerodynamics and aeroelasticity

A frequency response for linear time periodic (LTP) systems that exploits the one-to-one map induced by geometrically periodic signals is developed. This map is described by an integral operator, based on the GP (geometrically periodic) test input, and a generalized harmonic balance approach, based on an EMP (exponentially modulated periodic) input. The singular values or principal gains of the LTP operator are discussed, and the LTP principal gain diagram is described. Directional properties of the LTP operator are discussed, and notions of the domain and range spaces are presented. The framework of linear operators described has lead to the development of a comprehensive open-loop analysis theory for LTP systems, including a characterization of poles, transmission zeros, and their directional properties. >

Frequency response of linear time periodic systems

Application of the incremental harmonic balance method to cubic non-linearity systems

An efficient computational scheme for the analysis of periodic systems

Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method

Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.

C. E. Hammond

Papers

Efficient numerical treatment of periodic systems with application to stability problems