Dual-Frequency Vibration Absorption Using Delayed Resonator With Relative Position Measurement

A novel active vibration absorption technique, the Dual-Frequency Fixed Delayed Resonator, has been introduced recently as a unique way of suppressing undesired bitonal oscillations. It suggests a control force on a mass-spring-damper absorber in the form of a proportional position feedback with time delay. Its strengths consist of extremely simple implementation of the control algorithm and total vibration suppression of the primary structure against a dual-frequency force excitation. All the development work was done using absolute displacements of the absorber in the feedback. These displacement measurements, however, may be difficult to obtain and for some applications even impossible. Therefore, an easier way of absorber position detection, namely its relative measurement with respect to the primary structure, is proposed in this paper. Theoretical foundations for the Dual-Frequency Fixed Delayed Resonator are recapitulated and its implementation on a single-degree-of-freedom primary structure disturbed by a bitonal force is introduced utilizing both absolute and relative position measurement of absorber mass. Methods for stability and transient behavior analysis are presented. Properties acquired for the same system with these two different feedback are compared. Relative position measurement case is found to be more practical for most applications of the Dual-Frequency Fixed Delayed Resonator method.