COMPLEX DYNAMICS IN JOINTED STRUCTURES
Chris Verhoeven - (May 2022)
SUMMARY
The question of how to predict the damping in a non-proportionally damped structure has bothered the modal dynamics community for many decades. This thesis will not aim to solve this complex problem, but will instead dust of this topic by investigating the effect of non proportional damping.
This thesis will elaborate on three main challenges of dynamics containing joints. The first one is the effect of the closeness of natural frequencies in a bolted structure. Axisymmetric bolted structures contain close natural frequencies and damping which is unevenly distributed. The research will show the dynamic behaviour of a simple discrete MDOF system where two natural frequencies are very close to each other and the damping is non-proportionally distributed. This will show that increasing the closeness of the natural frequencies, to a certain extent, will also increase the complexity of the eigenvectors. It will also be shown that the amount of damping has an effect on the complexity of the eigenvectors. This understanding of the effect of damping on close modes induces an assumption that damping nonlinearity can be tuned such that modes shapes can be real or complex. Nonlinear damping can be achieved by joints as described earlier. However, it is critical that damping is identified correctly and so the research will deepen on techniques which are good for characterizing the nonlinear damping. Different nonlinear damping identification methods will be discussed and one of these will be used to develop a tool. This tool will be able to identify the nonlinear behaviour based on a set of FRF test data. Having explained how proportional damping changes the nature of the mode shapes from real to complex, and having elaborated a method for characterizing damping from data, a test structure will be designed. This test structure is a double cantilever beam and therefore contains a degree of symmetry which is assumed tunable by slightly altering one of the beams. The test structure also contains bolted joints which introduce nonlinear non proportional damping. This thesis will investigate the nonlinear properties of this structure and an attempt will be made to create complex modes by altering the natural frequencies of the first bending modes.