Stability test and dominant eigenvalues computation for second-order linear systems with multiple time-delays using receptance method. (March 2020)

• Record Type: Journal Article
• Authors: Zhang, Jia-Fan; Ouyang, Huajiang; Zhang, Ke-Wei; Liu, Hai-Min
• Is Part Of: Mechanical systems and signal processing. Volume 137(2020)
• Publication Date: 2020-03
• Subjects: Second-order system -- Receptance -- Multiple time-delays -- Retarded time-delay system -- Stability -- Dominant eigenvalue; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2019.05.064
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: A reduced characteristic function is obtained. Stability test and dominant eigenvalues computation are addressed. A contour integral method and a Newton-type method are used. Abstract: Stability analysis and dominant eigenvalues computation for second-order linear systems with multiple time-delays are addressed by using a reduced characteristic function and the associated characteristic matrix comprised of measured open-loop receptances. This reduced characteristic function is derived from the original characteristic function of the second-order time delayed systems based on a reasonable assumption that eigenvalues of the closed-loop system are distinct from those of the open-loop system. Then a contour integral is used to test the stability and provide the stability chart with respect to different displacement and velocity feedback time-delays, and a Newton-type method to compute the dominant eigenvalues via this characteristic function. The proposed approach also utilizes the spectrum distribution features of the retarded time-delay systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.