Abstract
Gyroscopic conservative dynamical systems may exhibit flutter instability that leads to a pair of complex conjugate eigenvalues, one of which has a positive real part and thus leads to a divergent free response of the system. When dealing with non-conservative systems, the pitch fork bifurcation shifts toward the negative real part of the root locus, presenting a pair of eigenvalues with equal imaginary parts, while the real parts may or may not be negative. Several works study the stability of these systems for relevant engineering applications such as the flutter in airplane wings or suspended bridges, brake squeal, etc., and a common approach to detect the stability is the complex eigenvalue analysis that considers systems with all negative real part eigenvalues as stable systems. This paper studies the cases where the free response of these systems exhibits a transient divergent time history even if all the eigenvalues have negative real part thus usually considered as stable, and relates such a behavior to the non-orthogonality of the eigenvectors. Moreover, the forced response of these system is addressed, highlighting how and in which cases, an unexpected amplification of the forced response may occur.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.