We study first-crossing problem of two-degrees-of-freedom (2DOF) strongly nonlinear mechanical oscillators analytically. The excitation is the combination of a deterministic harmonic function and Gaussian white noises (GWNs). The generalized harmonic function is used to approximate the solutions of the original equations. Four cases are studied in terms of the types of resonance (internal or external or both). For each case, the method of stochastic averaging is used and the stochastically averaged Itô equations are obtained. A backward Kolmogorov (BK) equation is set up to yield the failure probability and a Pontryagin equation is set up to yield average first-crossing time (AFCT). A 2DOF Duffing-van der Pol oscillator is chosen as an illustrative example to demonstrate the effectiveness of the analytical method. Numerically analytical solutions are obtained and validated by digital simulation. It is shown that the proposed method has high efficiency while still maintaining satisfactory accuracy.
First-Crossing Problem of Weakly Coupled Strongly Nonlinear Oscillators Subject to a Weak Harmonic Excitation and Gaussian White Noises
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 14, 2017; final manuscript received January 23, 2018; published online February 23, 2018. Assoc. Editor: Mohammed Daqaq.
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Wu, Y. J., and Wang, H. Y. (February 23, 2018). "First-Crossing Problem of Weakly Coupled Strongly Nonlinear Oscillators Subject to a Weak Harmonic Excitation and Gaussian White Noises." ASME. J. Vib. Acoust. August 2018; 140(4): 041006. https://doi.org/10.1115/1.4039244
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