Nonstationary Random Vibration Analysis of Wing with Geometric Nonlinearity Under Correlated Excitation

Abstract

An algorithm that integrates Karhunen-Loeve expansion (KLE), nonlinear finite element method (NFEM), and a sampling technique to quantify the uncertainty is proposed to carry out random vibration analysis of a structure with geometric nonlinearity under correlated nonstationary random excitations. In KLE, the eigenvalues and eigenfunctions of the autocovariance are obtained by using orthogonal basis functions, and the KLE for correlated random excitations relies on expansions in terms of correlated sets of random variables. The autocovariance functions of excitation are discretized into a series of correlated excitations, and then the structural response is carried out by using NFEM and sampling techniques. The proposed algorithm is applied to both rigid and flexible aircraft wings. Two different types of the boundary condition are studied for the flexible wing: fixed and large mass method (LMM). Results show that the geometric nonlinearity has a stiffening effect on the behavior of the aircraft wing, resulting in an oscillatory response with a lower amplitude, and changes the distribution of the random responses. The response due to LMM boundary condition that is closer to the actual conditions is smaller than the response obtained using fixed boundary condition.