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

✍ Scribed by Z.L. Huang; W.Q. Zhu


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
237 KB
Volume
204
Category
Article
ISSN
0022-460X

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✦ Synopsis


The exact stationary solutions of the averaged equations of stochastically 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 m 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 conditions with respect to m combinations of phase angles, the probability potentials of the exact stationary solutions of the equivalent stochastic systems are expanded into an m-fold harmonic series of m combinations of phase angles, and the exact stationary solutions are obtained for the case where the averaged equations belong to the class of stationary potential. Two examples are given to illustrate the application of the proposed procedure.