The envelope equation derived earlier is generalized to analyze a resonance among multiple modes by using the method of multiple scales, an excellent method for analyzing large-scale nonlinear systems. It is demonstrated through numerical simulations that the generalized envelope equation is valid for predicting the resonance phenomena themselves and also for examining the critical factors responsible for severe resonances. The factors chosen for study are the heaviness of the load, small dampings, and disturbances. The method is promising for the analysis of general multimode resonances.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Yorino et al. (1989) studied this question.
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