An analysis of the effects of the orientation angle of a surface crack on the vibration of an isotropic plate

Abstract

This paper proposes a vibration analysis for an isotropic plate containing an arbitrarily orientated surface crack as an enhancement to previous work on cracked plates for which the orientation of the crack angle was not included. The governing equation of motion of the plate with this enhanced crack modelling represents the vibrational response based on classical plate theory into which a developed crack model has been assimilated. The formulation of the angled crack is based on a simplified line-spring model and the cracked plate is subjected to transverse harmonic excitation with arbitrarily chosen boundary conditions. It is found that the vibrational characteristics of the plate structure can be affected significantly by the orientation of the crack in the surface plate. For reasons of comparison and validation a finite element model is used for a further modal analysis in order to corroborate the effect of crack length and crack orientation angle on the modal parameters i.e. the natural frequency and also the vibrational amplitude, as predicted by the analysis. The results show excellent agreement between the two methods.