**by Geoffrey E.B. Tan**

Many future space missions will require the use of large space structures with stringent operating requirements, such as precise geometrical configurations. Deployable structures are a cost-effective solution for these space missions. However, the joints used in deployable structures behave in a non-linear fashion, which makes vibration analysis and prediction difficult. Accurate dynamic models are required, on the other hand, to ensure that excessive vibrations do not compromise the mission objectives. It is thus important to develop methods to model such non-linear behaviour.

This dissertation is concerned with the non-linear vibration of cable-deployed structures. A non-linear modelling process is proposed and successfully applied to a cable-deployed structure, the Triangular Pantographic Mast. A physical model of this structure has been constructed and tested. The mast is deployed by reducing the length of a single cable and once deployment has been completed, prestressing of the whole structure locks the mast into position. It is established that the non-linear behaviour of the mast is affected considerably by these preloads, which act on the structural joints and thus change the amount of friction in the joints.

A quasi-static model of the mast which predicts the member forces during deployment and prestressing is developed and validated through experiments. A geometrically non-linear cable element is developed in order to facilitate this.

Modal tests are carried out on the mast to establish the variation of modal parameters with prestress levels, input force amplitudes, and gravity orientation. The components which most affect the vibration behaviour of the mast are identified and tested dynamically. A non-linear identification technique is used to make quantitative assessments of these components' behaviour. The technique is first validated on two simple systems with known non-linearities, and optimal identification strategies are thus identified.

A non-linear dynamic model is then derived. By using the describing function approach, the component non-linearities are quasi-linearized into equivalent stiffness and damping parameters, which are combined with the linear mathematical model. The equations of motion are solved using a modal superposition method. The dynamic model is validated against the experimental observations from the modal tests. It is concluded that in deployable structures whose joints are prestressed after deployment, friction is the major non-linear effect.

[Cambridge University | CUED | Structures Group | Geotechnical Group]

This page is maintained by rcb@eng.cam.ac.uk (last update 7 November 2003)