Chaos concepts in mechanical systems with clearances
This thesis considers the use of chaos concepts in investigating the dynamics of two discontinuously nonlinear mechanical systems having two degrees of freedom. The nonlinearity considered is in the form of a discontinuous stiffness effect, and can cause the systems to exhibit chaotic motion. The first system is a rotor system with a bearing clearance effect. The second is a nonlinear vibration absorber, comprising a conventional linear absorber and a linear snubber stiffness, which the auxiliary mass intermittently contacts. Numerical integration is used in solving the equations of motion for each system. Equivalent physical rigs are tested. Both the theoretical and experimental results are analysed using chaos techniques such as phase plane portraits, Poincaré maps, frequency spectra and bifurcation diagrams. Comparison made between the differently acquired results shows that fairly good correlation is obtained in both systems, for realistic values of damping. Periodic, quasiperiodic and chaotic responses are exhibited by both systems, for different combinations of system parameters, with the responses of the systems being extremely sensitive to changes in these parameters. Investigations of the rotor system concluded that quasi-periodic responses are only possible if there is some form of cross-coupling present. An effective discontinuously nonlinear absorber is developed, theoretically. A reduction in the amplitude of the second resonance peak of the linear absorber is achieved. This enables the primary system to be operated over a wider frequency range without reaching the large amplitudes to the second resonance. The non-linear absorber also has the effect of attenuating the response from the auxiliary mass. Fatigue analysis is carried out to investigate the effect of chaotic motions on mechanical components. The analysis reveals the subharmonic motions are more damaging than chaotic motions, which are in turn more damaging than simple fundamental responses.