Analysis and optimized design of an actively controlled two-dimensional delayed resonator

The absorption properties and active actuation of two-dimensional delayed resonators (2D-DR) are studied from various aspects. For a general 2D-DR, the actuation forces and energy supply needed for entire vibration absorption of a platform excited by a periodic force and torque are determined. For this purpose, a model describing the full absorber-platform dynamics is transformed into a form that allows to express the relevant design quantities as a function of the absorber’s parameters only. Subsequently, the parameters of the 2D-DR absorber, specifically the stiffness and damping of the connecting links, are optimized to turn the underlying three degree of freedom problem to a one degree of freedom problem. For this configuration, the stability and robustness in vibration absorption are studied. Based on the performed analysis, design rules are specified for the optimized 2D-DR design, including its positioning on the vibrating platform. A numerical case study demonstrates the 2D-DR absorber design and assessment of the operable frequency range for a specific set of voice-coil actuators.