VIBRATION EXPERIMENT AND NONLINEAR MODELLING RESEARCH ON THE FOLDING FIN WITH FREEPLAY

The influence of the freeplay on ground vibration responses of the folding fin and the nonlinear modelling of the freeplay, which exists in the joints connecting the inboard fin and the outboard fin, are studied in this paper. The first five modal parameters are obtained by hammer tests of the linear structure without freeplay. The sweep base excitation is then applied to the root-fixed folding fin with adjustable freeplay. The experimental results show that the existence of freeplay can lead to some nonlinear phenomena of the structure, such as a forward and backward sweep difference, a jump, multi harmonics, and a frequency shift. This kind of lumped nonlinearity has a huge influence on the first bending mode. For example, both the increase of the excitation magnitude and the decrease of the angle of freeplay will raise the fundamental frequency which gradually tends to the result of the linear structure without freeplay, but they have little effects on the second torsion mode compared with those on the first bending mode. The finite element model of the folding fin is established in the numerical simulation analysis and it is reduced by the developed model reduction method which is suitable for similar folding structures with lumped nonlinearity. The freeplay and contact of the joints are simulated by nonlinear torsional springs with the combination of linear and 3/2 order stiffness according to the Hertz theory. The linear part of the folding fin is verified firstly via comparing the first four frequencies and mode shapes computed from numerical analysis and the above hammer test. The dynamic response of the nonlinear structure under base excitation is calculated by Bathe's two-step implicit composite algorithm. The transfer functions obtained can simulate the frequency variation characteristics in the experiments, thus verifying the proposed nonlinear modelling method of the joint.