Considerations regarding superharmonic vibrations of a cracked beam and the variation in damping caused by the presence of the crack

Abstract

A closing crack causes the dynamic behaviour of a vibrating system to be significantly nonlinear.The main distinctive features of such a vibrating system are the appearance of sub- and superharmonic resonances, and the significant nonlinearity of the vibration responses at sub- and superharmonic resonances (displacement, acceleration, strain, etc.). The nonlinear effects are much more sensitive to the presence of a crack than are either the change of natural frequencies and mode shapes or the generation of high harmonics in the spectrum of vibration at principal resonance or far from resonance. Thus, the appearance of sub- and superharmonic resonances may prove to be useful, highly sensitive indicators of a crack's presence at very early stages of its nucleation; moreover, the level of response nonlinearity in this regime may provide a quantitative evaluation of damage parameters (type, size and location). At the same time, the manifestation of nonlinear effects depends not only on the crack parameters but also on the level of damping in a vibrating system. Recent experimental tests have revealed that crack nucleation and growth result in an increase of damping in a vibrating system. Consequently, the influence of crack's parameters upon the nonlinear effects should be determined while taking into account the change of damping in a vibrating system rather than assuming either constant damping or the total absence of damping. The empirical relationship between energy dissipated in a crack and nominal stress intensity factor range, estimated by curve-fitting experimental data, has been introduced into an FE model of a beam with a closing crack, and the influence of the damping level on the nonlinear dynamic behaviour of the beam was investigated.