<p>This paper presents a comprehensive analysis of a vibrating system with non-ideal excitation using the Incremental Harmonic Balance (IHB) method.&#xa0;The study focuses on the nonlinear dynamic behavior of a block (portal) foundation structure supporting an unbalanced rotating machine with limited power supply. The interaction between the motor and the structure, often overlooked in typical design practices, is thoroughly examined. The mathematical model incorporates the Sommerfeld effect, highlighting phenomena such as amplitude jumps, multi-mode interactions, and unstable solutions. Numerical and analytical methods, including the Runge–Kutta method, are employed to validate the findings. The results reveal significant insights into the dynamic behavior of non-ideal systems, providing a foundation for improved design and control strategies in engineering applications.&#xa0;The IHB method proves particularly useful in clearly identifying the influence of individual harmonics on the overall solution, as well as in facilitating the detection of internal resonance possibilities. The novelty of this study lies in the application of the Incremental Harmonic Balance (IHB) method to a rotary non-ideal system (RNIS), enabling the identification of complex nonlinear phenomena such as amplitude jumps, internal resonances, and unstable branches. The scientific contribution includes a validated methodology for analyzing and controlling such systems, which has not been previously applied in this context. It is also important to note that the IHB method requires the non-ideal excitation to be approximated by series expansions, which are valid only for sufficiently small values of the excitation parameters. This ensures that the analytical results remain accurate and comparable with numerical methods such as Runge–Kutta integration. In this study, the selected values satisfy these small conditions and justify the adopted approximation.</p>