矩阵摄动和Newmark-β逐步积分相结合的不确定性结构载荷识别

A method combining matrix perturbation and Newmark-βstepwise integration for load identification of uncertain structure

为了反演作用在不确定性结构上的动态激励上下界,在时域内建立了一个矩阵摄动和Newmark-β逐步积分相结合的载荷识别算法。首先依据矩阵摄动理论将动载荷近似表示为中值和摄动量相叠加的一阶泰勒多项式形式,然后引入Newmark-β逐步积分算法对振动学微分方程解耦,推导一个将输入载荷、输出响应和结构特性联系在一起的线性振动离散方程,借助该方程反求出动载荷的中值和摄动量,最终获得动载荷的上下边界。数值算例结果表明,该方法可以高效准确地重建载荷的上下边界,并具有优良的抗噪性能。

In order to reconstruct the upper and lower bounds of dynamic excitation applied on the uncertain structure,a method combining matrix perturbation and Newmark-βstepwise integration is establish.Firstly,matrix perturbation theory is used to express dynamic load in a first-order Taylor polynomial expansion.Then Newmark-βstepwise integration algorithm is introduced to decouple differential equation of structural dynamics in time domain.A linear discrete equation combining structural response,structural characteristics and dynamic load is set up.As a result the midpoint and first-order perturbation of dynamic load are calculated.Numerical examples indicate that the proposed method is able to identify force bounds at high speed and accuracy.Meanwhile,this method possesses strong noise resistance.