STABILITY ANALYSIS OF NONLINEAR SYSTEMS BY MULTIPLE TIME SCALING

摘要

The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary is obtained by using the multiple-time-scaling asymptotic- expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order ε3 (where ε is the order of amplitude of the unknown) are included in the solution. The solution indicates that there always exists a limit cycle. The limit cycle is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Com¬parisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.