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The effects of the Gaussian white noise excitation on structural safety due to erosion of safe basin in Duffing oscillator
with double potential wells are studied in the present paper. By employing the well-developed stochastic Melnikov condition
and Monte–Carlo method, various eroded basins are simulated in deterministic and stochastic cases of the system, and the ratio
of safe initial points (RSIP) is presented in some given limited domain defined by the system’s Hamiltonian for various parameters
or first-passage times. It is shown that structural safety control becomes more difficult when the noise excitation is imposed
on the system, and the fractal basin boundary may also appear when the system is excited by Gaussian white noise only. From
the RSIP results in given limited domain, sudden discontinuous descents in RSIP curves may occur when the system is excited
by harmonic or stochastic forces, which are different from the customary continuous ones in view of the first-passage problems.
In addition, it is interesting to find that RSIP values can even increase with increasing driving amplitude of the external
harmonic excitation when the Gaussian white noise is also present in the system.
The project supported by the National Natural Science Foundation of China (10302025 and 10672140).
The English text was polished by Yunming Chen. 相似文献
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