Nonlinear vibrations of large structures with uncertain parameters

Abstract

The effects of uncertainties on the nonlinear dynamics of complex structures remain poorly mastered and most methods deal with the linear case. This article deals with a model of a large and complex structure with uncertain parameters for the nonlinear dynamic case, and the reduction in the model discretized by the finite element method is obtained by reducing the degrees of freedom in the numerical model. This is achieved by the development of the unknown displacement vector on the basis of the eigenmodes; a particular attention is paid to the calculation of the nonlinear stiffness coefficients of the model. The method combines the stochastic finite element methods with a modal reduction class based on sub-structuring the component mode synthesis method. The reference method is the Monte Carlo simulation which consists in making several simulations for different values of the uncertain parameters. The simulation of complex and nonlinear structures is costly in terms of memory and computation time. To solve this problem, the perturbation method combined with the component mode synthesis reduction method significantly reduces the computational cost by preserving the physical content of the original structure. The numerical integration by the Newmark schema is used; the first statistical moments (mean and variance) of the nonlinear dynamic response are computed. Numerical simulations illustrate the accuracy and effectiveness of the proposed methodology.

Research on associated motion simulation method and platform of control rod driving mechanism

“…In addition, Newmark method is also widely used in geology and vibration. 10,11 The driving mechanism of nuclear reactor control rod is affected by coupling electromagnetic force and water resistance in the process of motion. At present, most of the studies are completed under a single action.…”

Vibration with non-linear damping. stochastic approach

“…This paper deals with the stochastic calculation of the vibration as a function of the variance mass parameter. Stochastic calculations are execute using the Monte Carlo simulation [5] and perturbation method [6]. The resulting curves for the studied parameters can find a practical application in the optimization of the systems.…”