Two-dimensional delayed resonator for entire vibration absorption

• Published in: Journal of sound and vibration Vol. 500; p. 116010
• Main Authors: Šika, Zbyněk, Vyhlídal, Tomáš, Neusser, Zdeněk
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 26.05.2021
• Subjects: Active vibration absorber; Delayed resonator; Planar uni-frequency absorber; Resonance; Stability; Time-delayed control; Resonance; Stability; Planar uni-frequency absorber; Time-delayed control; Active vibration absorber; Delayed resonator
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2021.116010

A one dimensional active vibration absorber with time delayed feedback known as delayed resonator proved to be well applicable for entire vibration absorption of mechanical structure at known excitation frequency. As the main and so far unique result, the delayed resonator concept is transferred from one dimensional to two dimensional vibration absorption. In the first step, an ideal two dimensional vibration absorber with three spring joints is designed with the three eigenfrequencies identical with the excitation frequency to be absorbed. Unlike in one dimensional case, the design imposes constraints on parameters of the two-dimensional absorber. In the second step, an active delayed position feedback is proposed at the three connecting joints with springs and dampers to turn a physical active absorber to the ideal uni-frequency absorber proposed in the first step. In particular, the task for the delayed feedback is to compensate the damping and virtually adjust the stiffness of the three active connecting elements. The proposed concept is analysed via frequency response of arising MIMO system as well as via spectral features of arising infinite-dimensional time delay system. The overall concept and design procedure are validated on a simulation case study.