<p>Vibrational sensors modelled as nonlinear cantilever beams with tip masses can achieve enhanced resolution when self-excited at higher resonant modes, necessitating mode-specific nonlinear modelling. This paper proposes a novel adaptive resonant control scheme that enables self-excitation of a weakly damped, base-excited cantilever beam with a tip mass at various desired resonant modes. The base excitation is defined as a nonlinear function of a second-order filter state, which uses the tip acceleration signal as feedback. An adaptive gain mechanism is implemented to regulate the oscillation amplitude of the tip to a predefined target. The sensor located at the tip facilitates mode switching by appropriately selecting filter parameters and the sign of the control gain. To target a specific mode, the filter frequency is tuned near the corresponding modal frequency, and the filter damping is chosen to be high to ensure single-mode excitation. A multiple time scale analysis is employed to study the system's dynamics. For each mode, the beam is self-excited to avoid jump and isolated resonance phenomena, and the steady-state responses are modelled using the Inverse Describing Function method applied to Padé and polynomial approximations of the response parameters. The resulting mode-specific models are validated against analytical beam models, with system parameters estimated via the Moore–Penrose pseudo-inverse method, demonstrating the accuracy and effectiveness of the proposed approach. To the best of the authors’ knowledge, this work represents the first experimental characterization of full dynamic behaviour of a nonlinear mechanical system across multiple resonance modes.</p>