In topology optimization (TopO), a mass distribution in a given design space and for known loads is computed, so that a defined criteria is minimized. TopO of dynamically loaded structures is still a challenge, and publications in the literature have in common that they are quite inefficient for an application to large FE models. The latter, however, is necessary in case of complex design spaces with given edges, bores and the like. This paper introduces a new method derived from the 'equivalent static load (ESL)' - approach, where quasistatic TopO and mode based time integration are performed in a loop. In contrast to the existing methods, damage is used as termination criteria in the loop for the iterative optimization procedure. The ESL for a next TopO step is derived from the most damaged area. Instead of a global optimum search, the FE model is systematically changed until the desired damage level is reached. Numerical examples underline the efficiency of the proposed method even with large FE models.