An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation

An analytical approach is presented for the forced vibration analysis of a plate containing a surface crack of variable angular orientation, based on three different boundary conditions. The method is based on classical plate theory. Firstly, the equation of motion is derived for the plate containing the angled surface crack with respect to one side of the plate and subjected to transverse harmonic excitation. The crack formulation representing the angled surface crack is based on a simplified line-spring model. Then, by employing the Berger formulation, the derived governing equation of motion of the cracked plate model is transformed into a cubic nonlinear system. The nonlinear behaviour of the cracked plate model is thus investigated from the amplitude–frequency equation by use of the multiple scales perturbation method. For both cracked square and rectangular plate models, the influence of the boundary conditions, the crack orientation angle, crack length, and location of the point load is demonstrated. It is found that the vibration characteristics and nonlinear characteristics of the plate structure can be greatly affected by the orientation of the crack in the plate. Finally the validity of the developed model is shown through comparison of the results with experimental work.