Importance of structural damping in the dynamic analysis of compliant deployable structures

Abstract

Compliant mechanisms such as tape springs are often used on satellites to deploy appendices, e.g. solar panels, antennas, telescopes and solar sails. Their main advantage comes from the fact that their motion results from the elastic deformation of structural components and the absence of actuators or external energy sources. The mechanical behaviour of a tape spring is intrinsically complex and nonlinear involving buckling, hysteresis and self-locking phenomena. In the majority of the previous works, dynamic simulations were performed without any physical representation of the structural damping. These simulations could be successfully achieved because of the presence of numerical damping in the transient solver. However, in this case, the dynamic response turns out to be quite sensitive to the amount of numerical dissipation, so that the predictive capabilities of the model are questionable. In this work based on numerical case studies, we show that the dynamic simulation of a tape spring can be made less sensitive to numerical parameters when the structural dissipation is taken into account. I INTRODUCTIONWith the extensive development of small satellites and cubesats dedicated to low-cost missions, the mass reduction of the components is paramount. However, the power reduction due to the miniaturisation of electronic equipment does not follow the same downward slope. Thus, covering only the external surface of the satellite with solar cells might not provide enough power and be too restrictive, hence the necessity for a reliable but cheap and simple means to deploy large solar panels. This, however, brings another major problem that must be solved: the packaging of large structures into the confined space inside the fairing of launch vehicles. In order to address these challenges, deployable structures have been developed and a brief listing of the most common structures can be found in [1]. This paper will focus on those belonging to the compliant mechanisms category and in particular on tape springs.A tape spring is a thin strip curved along its width commonly known as a Carpenter tape and used in the everyday life as tape measures. Nowadays, it finds applications in the space domain for the deployment of appendices such as solar panels, antennas, telescopes and solar sails. Since they belong to the category of compliant mechanisms, they rely only on elastic energy that is stored during the folding and then naturally released when deployed. Indeed, a possible equilibrium state when the tape spring is free of constraints is the straight configuration, which is sought as a deployed configuration for many space applications. This characteristic also brings forward the fact that no source of external energy is required for the deployment and hence the passive and selfactuated behaviours of these devices.Their motion results from the deformation of structural components only and not from the sliding between contact surfaces as in usual hinges or prismatic joints. It implies that tape springs do not requ...

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