Estimation and veering analysis of nonlinear resonant frequencies of cracked plates

In this paper, veering phenomena in the nonlinear vibration frequencies of a cantilevered cracked plate are investigated, and an efficient method for estimating these frequencies is proposed. Of particular interest is the vibration response in parameter regions where the natural frequency loci show veerings. For a representative finite element model, it is shown that the veerings due to crack length variation involve the switching of mode shapes and modal interactions. The nonlinearity caused by the crack closing effect is then introduced, and its effect on the vibration response near the veerings is discussed. The nonlinear forced response analysis is carried out using a hybrid frequency/time domain method, which is based on the method of harmonic balance. The nonlinear vibration response near loci veerings and crossings due to the variation of crack length is investigated in detail. Finally, a novel method for estimating the nonlinear resonant frequency is introduced by generalizing the concept of bilinear frequency approximation, and the method is validated with the results of nonlinear forced response analysis for several veering regions.