Open AccessA CONDITIONAL STOCHASTIC PROJECTION METHOD APPLIED TO A PARAMETRIC VIBRATIONS PROBLEM
Author(s) -
W. Brząkała,
Aneta Herbut
Publication year - 2014
Publication title -
journal of civil engineering and management
Language(s) - English
Resource type - Journals
eISSN - 1822-3605
pISSN - 1392-3730
DOI - 10.3846/13923730.2014.914105
Subject(s) - polynomial chaos , monte carlo method , parametric statistics , mathematics , vibration , mathematical analysis , random vibration , discretization , conditional expectation , polynomial , physics , statistical physics , quantum mechanics , statistics , econometrics
Parametric vibrations can be observed in cable-stayed bridges due to periodic excitations caused by a deck or a pylon. The vibrations are described by an ordinary differential equation with periodic coefficients. The paper focuses on random excitations, i.e. on the excitation amplitude and the excitation frequency which are two random variables. The excitation frequency ωL is discretized to a finite sequence of representative points, ωL,i Therefore, the problem is (conditionally) formulated and solved as a one-dimensional polynomial chaos expansion generated by the random excitation amplitude. The presented numerical analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben-Ahin bridge). The results obtained by the use of the conditional polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation (truly two-dimensional, not conditional one). The convergence of both methods is discussed. It is found that the conditional polynomial chaos can yield a better convergence then the Monte Carlo simulation, especially if resonant vibrations are probable.