Previously, the authors proposed a solution technique based on the principle of harmonic balance. The technique requires the excitation force to be periodic. This is, in some cases, a restriction. So, another technique free from this restriction is here proposed and applied to beams. The modified technique can be classified as a time-domain technique, two variations of which are examined. The former approach is based on the usual least-squares method, whereas the latter is based on solving a minimization problem with constraints. The latter usually yields better results, however an iteration procedure is needed which requires initial values for parameters. To obtain the initial values, the authors use the first method. The applicability of the proposed technique is validated by numerical simulations and by experiments.