On the analysis of the efficiency of the spectral vibration diagnostic method for detecting fatigue damage to elements: Report 2. Bending vibrations, Analytical solution

摘要

A possible efficiency In the use of the harmonic analysis of elastic rod deformation cycle under free or resonance oscillations is considered to estimate the fatigue damage. In modelling the fatigue damage as the material discontinuity which isresponsible for the difference In the modulus of elasticity in tension and compression and In determining the rod strain energy induced by the presence of a crack, the expressions for the relative change in the rod rigidity with edge and surface cracksbeing available have been derived based on the statements of the linear elastic fracture mechanics. By applying the asymptotic nonlinear mechanics method. the solution of the differential equation of vibrations of the rod whose nonlinearity is caused bythe "breathing" of the formed discontinuity of the material has been obtained to a second approximation. The material discontinuity due to fatigue damage has been shown to cause a constant component and even harmonics manifested clearly in the cycle ofthe rod deformation. The values of the constant and amplitudes of the even harmonics and primarily. the second harmonic, can be an efficient diagnostic parameter of the fatigue damage.