The primary mirror of the Ariel space telescope (an ESA M class mission aimed at the study of exoplanets, scheduled for launch in 2029) is an elliptical off-axis paraboloid. Like the entire telescope, it is built of aluminum. As a massive part of the payload, as well as one of the most delicate components of the telescope, this mirror has to be accurately designed, in order to minimize its mass while not degrading its optical performances. This paper discusses the optimization study of the primary mirror of Ariel. Starting from its optical and geometrical specifications, we have run an iterative process based on FEA dynamic analyses, in order to compute the first ”free-free” eigenfrequencies while varying the three fundamental parameters of the honeycomb structure of the mirror - the thickness of the ribs, the outer edge, and the reflecting surface. Later, the optimization routine has been improved by adding the honeycomb geometry as a variable parameter. As a result, the best configurations is identified as the ones giving the higher ratios of the first relevant eigenfrequency divided by the mass.
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