This article presents a methodology to address the transient dynamic response of systems containing rotors, structures and foundations interacting with soil profiles. These complex systems have been playing an ever-increasing role in the production of sustainable energy by onshore and offshore wind turbines. Two subsystems are considered. A Laval rotor governed by a set of time domain nonlinear equations on a rigid foundation is subsystem I. A linear structure resting on a viscoelastic half-space is subsystem II. The Finite Element Method models the structure. The soil dynamics in the frequency domain is characterized by a set of flexibility functions obtained by the Boundary Element Method. Time domain equations governing the subsystem II are determined by extracting modal parameters from frequency response functions describing the coupled soil-structure response. A staggered solution procedure couples the two subsystems. The method is used to examine the unbalanced response of a rotor is supported by a structure-foundation-soil system. The analysis evaluates how rotor external damping and soil geometric damping affect the torque requirement to pass through resonances.