On stability domains of nonconservative systems under small parametric excitation

Abstract

A linear multi-parameter nonconservative system under small periodic parametric excitation is considered. Approximations of the stability domain in the parameter space are derived in the cases, when the corresponding autonomous system has a zero eigenvalue or a pair of complex conjugate imaginary eigenvalues. Formulae of the approximations use information on the unperturbed autonomous system and derivatives of system matrices with respect to parameters. Singularities arising on the stability boundary are analyzed. As a numerical application, stability of a pipe conveying pulsating fluid is studied.