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First-passage problem of a class of internally resonant quasi-integrable Hamiltonian system under wide-band stochastic excitations |
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| Affiliation: | 1. Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, Praha 8 – Karlín CZ 186 75, Czech Republic;2. Texas A&M University, Department of Mechanical Engineering, 3123 TAMU, College Station, TX 77843-3123, United States of America;1. Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, Ecole des Ponts ParisTech, IFSTTAR, F-77455 Marne La Vallée, France;2. Université Paris-Est, MAST, SDOA, IFSTTAR, F-77447 Marne La Vallée, France;1. Department of Mathematics G. Castelnuovo, Sapienza Roma University, Roma, Italy;2. In Unam Sapientiam, Roma, Italy;3. IAPS, Istituto Nazionale di Astrofisica INAF, Roma, Italy;4. IASF, Istituto Nazionale di Astrofisica INAF, Palermo, Italy;5. INFN, Sezione Roma1, Roma, Italy |
| Abstract: | In this paper, first-passage problem of a class of internally resonant quasi-integrable Hamiltonian system under wide-band stochastic excitations is studied theoretically. By using stochastic averaging method, the equations of motion of the original internally resonant Hamiltonian system are reduced to a set of averaged Itô stochastic differential equations. The backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are established under appropriate boundary and (or) initial conditions. An example is given to show the accuracy of the theoretical method. Numerical solutions of high-dimensional backward Kolmogorov and Pontryagin equation are obtained by finite difference. All theoretical results are verified by Monte Carlo simulation. |
| Keywords: | First-passage problem Internal resonance Wide-band stochastic excitation Stochastic averaging method |
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