First-passage time of an inverted pendulum subject to high frequency harmonic and Gaussian white noise excitations

• Published in: Probabilistic engineering mechanics Vol. 24; no. 2; pp. 128 - 134
• Main Authors: Huang, Z.L., Zhu, Z.Q., Jin, X.L.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.04.2009; Elsevier
• Subjects: Exact sciences and technology; First-passage time; Fundamental areas of phenomenology (including applications); Gaussian white noise; High frequency harmonic excitation; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Physics; Sciences and techniques of general use; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Gaussian white noise; High frequency harmonic excitation; First-passage time; Inversed pendulum; Averaging method; Energy method; Itô equation; Equation of motion; Partition method; Random excitation; Modeling; Direct method; Gaussian noise; White noise; First passage time; Reduced order systems; Non linear effect; Sinusoidal excitation; Reliability; High frequency; Random vibration; Stochastic equation
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2008.03.001

The first-passage time of an inverted pendulum subject to a combination of high frequency harmonic excitation and Gaussian white noise excitation is investigated. The high frequency harmonic excitation term is simplified to an equivalent autonomous nonlinear stiffness term by using the method of direct partition of motions. Then, the equations of motion of the equivalent system are reduced to an averaged I t o ˆ stochastic differential equation by using the stochastic averaging method of energy envelope. After that, a backward Kolmogorov equation governing the conditional reliability function of first-passage time is established by using the averaged I t o ˆ equation. The conditional reliability function and the conditional probability density of first-passage time from numerical solution of the backward Kolmogorov equation agree well with those from digital simulation of the equivalent system. The effects of system parameters on the conditional reliability function and the conditional probability density of the system are discussed.