Abstract
The method of quasi-conservative averaging, or the stochastic averaging of energy envelope, is extended to a system with a double-well potential subjected to both the external and parametric non-white noise excitations. Instead of using the power spectral densities, the correlation functions of the excitation processes are used directly so that the averaging procedure can be performed for different types of motions appearing in the system with a double-well potential. The obtained Markov process of the energy envelope allows to carry out the dynamic analysis of the system, such as to assess the asymptotic behaviors at the boundaries, to find the probability density of the response, and to investigate the transition of the system motion between the two wells, as done in the present paper. Furthermore, the proposed procedure can be applied not only to systems with double-well potentials, but also to those with potentials of more complicated shapes.
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