Force Reconstruction for Nonlinear Structures in Time Domain

Abstract

With growing complexity of mechanical structure, nonlinear factors existing in the structure have drawn much attention in recent years. Meanwhile, accurate information of dynamic force is an important index for analyzing nonlinear mechanical structure. However, these data are always difficult and even impossible to be measured directly. Therefore, in this paper, a novel reconstruction strategy is proposed to calculate the external force of the nonlinear structure on the basis of measured response at the reference position. For the reconstruction strategy, the force reconstruction equation of nonlinear structure is established by the nonlinear state-space model, and nonlinear subspace identification (NSI) algorithm is utilized to estimate coefficient matrices of the nonlinear state-space model to form the transfer matrix. And then, considering the illcondition of the transfer matrix, the regularization method combined with the generalized cross-validation criterion is utilized to solve the ill-posed reconstruction equation to obtain the unknown external force. Numerical study is conducted to illustrate the feasibility of the reconstruction strategy. The results demonstrate that the proposed reconstruction strategy can be utilized to accurately obtain the external force of the nonlinear structure.