Time-domain quasilinear identification of nonlinear dynamic systems

Abstract

A time-domain linear modal identification technique is applied to identify some highly nonlinear dynamic systems. The modal concept is used to identify such nonlinear systems with the understanding that the resulting modes are only a mathematical representation of the series solution of the nonlinear system under consideration. Naturally, these identified modal parameters are not unique for nonlinear systems, since they are functions of the systems' amplitudes and hence referred to as quasilinear. The approach presented in this paper can be useful in predicting signs of nonlinearitie s when linearity is assumed. It can also be used to analyze and understand the types of nonlinearitie s in nonlinear systems through successive identifications at different levels of response. Nomenclature / = frequency, Hz Fj = force in restoring force element / M = mass m - number of degrees of freedom of the identification math model n — number of harmonics 1/2(0) = measurement noise vector Ni = modal vector for noise representation p = number of degrees of freedom of system under identification q = number of degrees of freedom allowed for measurements noise r/ = /th characteristic root for noise representation ( x(t)} = linear system response vector {y(t)} = nonlinear system response vector z(t) = displacement in restoring force element a/ = /th characteristic root for harmonics F = /th modal vector of harmonics f/ = /th damping factor, % {6} = angular displacement ( \l/j} = /th linear (or equivalent linear) modal vector ITD = Ibrahim time-domain modal identification technique NMO = number of modes allowed in the identification math model SDOF = single-degree-of-freedom system TDOF = two-degree-of-freedom system