Topology optimization is increasingly used as a design tool in engineering. Within structural mechanics, most applications focus on statics. An extension to time-domain (transient) dynamics will have many useful applications, but this is currently hindered by high computational costs. The goal of this research is to reduce these costs by applying model order reduction. In model order reduction, the full coordinates of a system are approximated by a much smaller number of reduced coordinates and associated basis vectors. A few options for these vectors will be discussed. It is shown that using load-based methods results in high accuracy, especially the Ritz vector method. In the total optimization this leads to significant reduction of both CPU-time and memory requirements.