用时域仿真求解一随机振荡系统的水准跨越率

CALCULATION OF THE LEVEL CROSSING RATES OF A RANDOM OSCILLATION SYSTEM BY TIME DOMAIN SIMULATION

要为获得一在随机激励下的非线性结构系统的响应的向上水准跨越率而进行了蒙特卡罗仿真。该结构系统的非线性包括Duffing刚度和考虑海流存在时的Morison拖力,四阶Runge-Kutta法被用来对该结构系统在不同海流速度下的运动微分方程进行数值积分,得到了响应值的一阶导数以及响应值与响应值一阶导数的联合概率密度,接下来利用著名的R ice公式计算了系统响应的向上水准跨越率。这是首次对该类型非线性系统进行数值仿真,并且获得了系统响应的水准跨越率的精确预报。该跨越率值是求取许多有关响应统计和可靠性分析的重要数据的关键。

Monte Carlo simulation is performed in order to get the level up-crossing rates of the responses of a nonlinear structural system under random excitation.The nonlinearities in the structural system include the Duffing stiffness and Morison drag force when an ocean current is present.The differential equation of motion of the structural system under different ocean current conditions are numerically integrated via a fourth-order Runge-Kutta scheme.The first derivatives of the responses and the joint probability densities with respect to the responses and their first derivatives are obtained.The system response level up-crossing rates are then calculated by using the well known Rice formula.To the authors'knowledge,no digital simulation has ever been performed that allows an accurate prediction of the level crossing rates of the responses of the type of nonlinear system considered here.