Application of an improved cell mapping method to bilinear stiffness aeroelastic systems

Abstract

A “mapping trajectory pursuit (MTP)” is introduced to improve the cell mapping techniques based on spatial Poincaré sections. Such an improvement enables the cell mapping method to determine the exact properties of all cells with less computer memory and computational time. For the purpose of prediction of the stability boundary as a function of initial conditions (domains of attraction), an initial condition region is defined besides the domain of interest. The proposed CM method is used to analyse the aeroelastic behaviour of an aeroelastic system with bilinear structural nonlinearity. Different types of motions including damped stable motion, limit cycle oscillation, complicated periodic motion, chaotic motion and divergent flutter are determined as a function of initial conditions (domains of attraction). The results compare well with that from stability analysis of the system. The bifurcation diagrams are also obtained using the method to reveal the influence of disturbances on the dynamical behaviour of the system over a broad range of air speed.