EXACT STATIONARY SOLUTIONS OF AVERAGED EQUATIONS OF STOCHASTICALLY AND HARMONICALLY EXCITED MDOF QUASI-LINEAR SYSTEMS WITH INTERNAL AND OR EXTERNAL RESONANCES/

The exact stationary solutions of the averaged equations of stochastic ally and harmonically excited n-degree-of-freedom quasi-linear systems with m internal and/or external resonances are obtained as functions of both n independent amplitudes and nl combinations of phase angles. To make the solutions more general, the equivalent stochastic systems of the averaged equations are obtained by using the differential forms and exterior differentiation. By considering the periodic boundary co nditions with respect to m combinations of phase angles, the probabili ty potentials of the exact stationary solutions of the equivalent stoc hastic systems are expanded into an m-fold harmonic series of m combin ations of phase angles, and the exact stationary solutions are obtaine d for the case where the averaged equations belong to the class of sta tionary potential. Two examples are given to illustrate the applicatio n of the proposed procedure. (C) 1997 Academic Press Limited.