A new approach in the analysis of linear systems with periodic coefficients for applications in rotorcraft dynamics

Abstract

AbstractA numerical technique for the stability analysis of linear mechanical dynamic systems with periodically varying parameters is proposed. The technique is based on representation of the solution vector in terms of Chebyshev polynomials defined over the principal period. Two formulations have been presented. The first formulation is suitable for systems described by state space equations, while the second can be applied directly to a set of second order equations with periodically varying mass, damping and stiffness matrices. As an illustrative example, the flap-lag stability of a multi-bladed rotor is examined. The numerical accuracy and efficiency of the proposed technique is compared with standard numerical codes based on Runge-Kutta, Adams-Moulton and Gear algorithms. The results indicate that the suggested approach is by far the most efficient one, particularly for systems with larger dimensions.