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A discrete time control algorithm using the damped least squares isintroduced for acceleration and energy exchange controls in nonlinear vibratingsystems. It is shown that the damping constant of least squares and samplingtime step of the controller must be inversely related to insure that vanishingthe time step has little effect on the results. The algorithm is illustrated ontwo linearly coupled Duffing oscillators near the 1:1 internal resonance. Inparticular, it is shown that varying the dissipation ratio of one of the twooscillators can significantly suppress the nonlinear beat phenomenon.

Acceleration Control in Nonlinear Vibrating Systems based on Damped Least Squares