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Abstract
The exact stationary solutions of the averaged equations of stochastically and harmonically excitedndegree-of-freedom quasi-linear systems withminternal and/or external resonances are obtained as functions of bothnindependent amplitudes andmcombinations 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 conditions with respect tomcombinations of phase angles, the probability potentials of the exact stationary solutions of the equivalent stochastic systems are expanded into anm-fold harmonic series ofmcombinations of phase angles, and the exact stationary solutions are obtained for the case where the averaged equations belong to the class of stationary potential. To examples are given to illustrate the application of the proposed procedure.
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