Continuous earthmoving machines, such as bucket-wheel excavators (BWEs), are the largest mobile terrestrial machines exposed to the working loads of a periodic character. This paper aims to launch a new idea regarding the preservation of the load-carrying structures of these machines by the means of implementing a controllable frequency-controlled drive of the excavating device. Successful implementation of this idea requires a detailed analysis of the dynamic response of the load-carrying structure in order to determine the domains of frequency of revolutions of the bucket-wheel-drive electromotor (FREM) where the dynamic response of the structure is favorable. The main goal of the presented research was the development of a unique three-step method for the identification of the FREM ranges, where the vibroactivity of the load-carrying structure is within the allowed boundaries. A methodologically original study of the dynamic response was conducted on a unique dynamic model of the BWE slewing superstructure that allows for continuous variation of the FREM, i.e., of the frequency of excitation caused by the forces resisting the excavation. Validation of the spatial reduced dynamic model of the slewing superstructure and the corresponding mathematical model, as well as the overall approach to the determination of the dynamic response, were performed by the means of vibrodiagnostics under the real exploitation conditions. Application of the developed method has yielded: (1) the resonant-free FREM domains; (2) the FREM domains, where the structure is not exposed to the excessive dynamic impacts; and (3) the frequency ratio ranges defining the resonant areas. Additionally, the results of the research have pointed out that the resonant-free state represents a necessary but insufficient condition for the proper dynamic behavior of the BWE slewing superstructure.