A Conditional Stochastic Projection Method Applied to a Parametric Vibrations Problem

Abstract

Abstract. 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 L ω is discretized to a finite sequence of representative points,ω . 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.

Sensitivity Analysis of Stress State of Welded Tanks

“…4 was evaluated for one hundred simulation runs of the LHS method [4,5]. It may be noted that advanced numerical simulation methods such as Monte Carlo are often used in reliability studies of building structures, see, for e.g., [6][7][8][9][10][11][12]. It is evident from the comparison of stress in the left and right hand side of Fig.…”

Nonlinear vibrations of CFRP cables excited by periodic motions of supports in cable-stayed bridges

“…They developed theoretical models for the vibrations of the cables subjected to support excitations, respectively. In general, vibration models can be classified into a single-cable vibration model (Lilien and Pinto Da Costa, 1994; Chen et al., 2002; Sun et al., 2003; Wu et al., 2003; Mei et al., 2007; Ying et al., 2007; Wang and Zhao, 2009; Kang et al., 2016; Ouni and Kahla, 2012; Brzakala and Herbut, 2014; Sun et al., 2014; Qian et al., 2014; Guo et al., 2016; Warminski et al., 2016) and cable-deck coupling vibration model (Luo et al, 2010; Kang et al., 2012; Sun et al., 2017). In addition, support excitations include the following: horizontal excitation at the upper support of the cable, vertical excitation at the lower support or axial excitation.…”