### Abstract

Oscillations in machines are invariably nonlinear. This is either because of inertial coupling effects between different motions of the moving components, material and constitutive phenomena giving rise to stiffness modifications, nonlinear dissipation mechanisms, large deflections, or, as is most likely, some sort of combination of all of these. The net effect of nonlinear vibrations is that at best the machine may well behave a little differently from the way the designer intended, or at worst, in a manner which renders it completely unsuitable for the job. The extent of such problems depends on the nature and the scale of the nonlinearities that are present but it is safe to say that nonlinear oscillations can rarely be completely overlooked in precision machinery analysis and design. The unifying theme in this paper is pendulum motion, firstly in the case of a mobile gantry crane for container stacking where we wish to minimise such motion and converge on a target, and then secondly in the case of a vibration absorber in which we choose to initiate pendulum motion within a special absorber, for the purposes of vibration minimisation. The third example involves the potential for pendulum motion at a very much larger scale and summarises the main control problem that is likely to be encountered in a fully deployed momentum exchange propulsion tether operating in space. The paper discusses the general mathematical issues that pertain to pendulum motion in each of the three cases. This motion is investigated initially in the context of the mobile gantry crane, in the form of a basic three dimensional dynamical model. A feedback linearised controller is shown to offer some advantages for the control of such a system and then a simulation based on data from a practical implementation of this within a real-time control system on a 1/10 laboratory scale model is discussed. It is recalled that the real-time effectiveness of the controller can be compromised by relatively slow sensing and data logging hardware but that despite this some useful performance gains can still be obtainable using this sort of control strategy. The second example comprises an autoparametric vibration absorber and here it is shown how even a simple hunting controller can exploit the mode-locking and wide detuning region effects inherent in autoparametric systems. Further experimental results are discussed in the case of a hunting controller for detuning a vertically oriented parametrically excited pendulum in order to exploit and enhance the powerful and persistent absorption available during autoparametric interaction. The paper concludes with a summary review of the third problem in which the theoretical attitude dynamics of a motorised momentum exchange space propulsion tether are summarised and it is shown that they need to be controlled for reliable and optimal payload velocity boost from both circular parking orbits and elliptical transfer orbits about the Earth.

Original language | English |
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Pages (from-to) | 185-212 |

Number of pages | 28 |

Journal | Meccanica |

Volume | 38 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2003 |

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### Keywords

- Pendulum motion
- nonlinear oscillations
- parametric vibrations
- autoparametric vibrations
- gantry cranes