Application of Asymptotic and Numerical Methods to Determine Stability Boundaries of Distributed Systems in a Flow

• Published in: Cybernetics and systems analysis 2022-03, Vol.58 (2), p.233-241
• Main Authors: Kaliukh, I., Lebid, O.
• Format: Article
• Language: English
• Subjects: Air-turbines; Artificial Intelligence; Asymptotic methods; Asymptotic properties; Bending; Computer networks; Control; Flow stability; Flutter; Flux density; Frequency ranges; Inclination angle; Mathematics; Mathematics and Statistics; Methods; Numerical analysis; Numerical methods; Perturbation; Processor Architectures; Software Engineering/Programming and Operating Systems; Stability analysis; Stiffness; Stress concentration; Systems Theory
• ISSN: 1060-0396; 1573-8337
• DOI: 10.1007/s10559-022-00455-0

The reasons and the set of parameters leading to aeroelastic flutter vibrations in distributed systems (DS) are investigated on the basis of asymptotic and numerical methods. The instability is caused by the combined influence of three factors: the drift of perturbations along the DS in the flow, bending stiffness, and the influence of the inertial force, which is a distributed load moving along the DS. An increase in the tensile force and bending stiffness of the DS shifts the instability to a higher-frequency range of vibrations. An increase in the relative flux density and the relative length of the DS expands the region of instability. The presence of the angle of inclination of the DS to the flow adds peculiarities to the balance of forces acting on the DS and to the formation of the boundary ofstability and instability of regions. However, it is not possible to correctly assess its influence within the framework of the considered model and a more detailed further consideration is required. The configuration of the DS in the unstable region indicates the concentration of stresses near its upper end. The results obtained for small angles of inclination of the DS to the flow are consistent with the available results obtained by other authors.