Nonstationary response of nonlinear systems using equivalent linearization with a compact analytical form of the excitation process

A new method based on equivalent linearization approaches is presented for estimating the nonstationary response of a class of nonlinear multi-degree-of-freedom systems subjected to nonstationary excitations. The highly efficient method is based on creating a compact analytical approximation of measured nonstationary excitation process data through use of a two-stage decomposition procedure. The analytic data condensation of the excitation process is performed in two stages; (1) by performing the Karhunen–Loeve spectral decomposition on the covariance matrix of the input random process to obtain the dominant eigenvectors, and (2) by fitting these eigenvectors with orthogonal polynomials to produce a truncated series of analytically approximated eigenvectors. The efficiency and accuracy of the method is demonstrated through simulation with synthetically generated excitation data as well as measured data from a real-world physical process. Although the decomposition procedure used can characterize very general input processes, because the equivalent linearization technique requires the Gaussian assumption of the response process, the constraint on applying this approach is similar to the constraints on all other equivalent linearization techniques. However, the additional freedom gained from being able to work with data-based nonstationary random processes is a significant addition to this area of research.