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Studies on structural safety in stochastically excited Duffing oscillator with double potential wells

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Abstract

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.

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Authors and Affiliations

  1. Institute of Applied Mechanics, SAA, Zhejiang University, Hangzhou, 310027, China

    Chunbiao Gan

  2. College of Mechanical and Energy Engineering, Zhejiang University, Hangzhou, 310027, China

    Shimin He

Authors
  1. Chunbiao Gan
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  2. Shimin He
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Correspondence to Chunbiao Gan.

Additional information

The project supported by the National Natural Science Foundation of China (10302025 and 10672140).

The English text was polished by Yunming Chen.

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Gan, C., He, S. Studies on structural safety in stochastically excited Duffing oscillator with double potential wells. Acta Mech Sin 23, 577–583 (2007). https://doi.org/10.1007/s10409-007-0091-4

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  • DOI: https://doi.org/10.1007/s10409-007-0091-4

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