Vibration Response of Cracked Cantilevered Plates Near Natural Frequency Veerings

Abstract

In this paper, the linear and nonlinear vibration response of a cracked cantilevered plate is investigated as the crack location or crack length is varied. 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. A hybrid-interface method of component mode synthesis is employed to generate a compact reducedorder model of the system while retaining the crack surface degrees of freedom (DOF) as physical DOF so that the nonlinear boundary conditions caused by the contact may be enforced. 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. Furthermore, an alternative method for estimating the nonlinear resonant frequency is introduced by extending the bilinear frequency approximation, and its advantages and limitations are addressed.