<p>Dynamic vibration absorbers (DVAs) are widely used for resonance control. Non-resonant forced vibration is also prevalent in engineering applications. Although its amplitude is smaller, it can still lead to structural fatigue and failure over long periods. However, its control has not been systematically and thoroughly investigated. This study pioneers the systematic control of non-resonant forced vibration using a tuned mass damper (TMD). A coupled dynamic model of the damped primary system and the TMD is established. The vibration suppression mechanism under non-resonant conditions is revealed through analytical methods. A quantitative relationship between damping and tuning frequency is constructed. The influence of parameters on control performance and the effective tuning frequency domain is analyzed. A feasible parameter domain for simultaneously suppressing resonant and non-resonant forced vibrations is determined. The results show that the TMD can induce anti-resonance in the non-resonant region, and forced vibration is effectively suppressed. Appropriate parameter selection can enhance the vibration control effect and broaden the effective tuning frequency range, enabling both resonance and non-resonant control. Experiments are conducted to verify the correctness of the theoretical results. This study extends the application of control theory of DVAs and provides theoretical guidance for the control of non-resonant vibrations.</p>