Phase-controlled selective vibration switching in 2DOF harmonically driven systems

Antiresonance is commonly exploited to suppress the response of a selected coordinate in multi-degree-of-freedom mechanical systems. In conventional dynamic vibration absorbers, however, the secondary-mass motion is typically treated as a consequence of absorber operation rather than as an independently switchable output. This study investigates a two-degree-of-freedom system subjected to two harmonic forces and develops explicit conditions under which the suppressed response can be switched between the two physical coordinates by changing only the relative phase of the excitations. Antiresonance is formulated as a zero of the selected steady-state coordinate response while the dynamic-stiffness matrix remains nonsingular. Closed-form expressions for the coordinate antiresonance frequencies, phase force ratios, switching frequencies, and their existence conditions are derived, and the relation of the formulation to the general frequency-response framework is discussed. The proposed phase-control strategy operates at fixed excitation frequency, fixed force amplitudes, and unchanged mechanical parameters, thereby avoiding resonance traversal during switching. Numerical simulations verify the analytical conditions and quantify the combined influence of viscous damping and phase-angle error by means of a normalized residual-amplitude ratio. The results show that damping shifts the phase corresponding to minimum residual response and progressively weakens the ideal cancellation mechanism. A dual-trough vibratory conveyor is considered as a motivating application. The present results establish theoretical and numerical feasibility; experimental validation of the drive and phase-control implementation remains a subject of future work.