Application of nonlinear resonances for the diagnostics of closing cracks in rodlike elements

Abstract

The vibrations of elastic bodies with closing cracks are essentially nonlinear. As a specific feature of these vibrations, one can mention the manifestation of so-called nonlinear effects, e.g., nonlinear (i.e., sub-and superharmonic) resonances and the nonlinearity of vibrations for these resonances. The proposed method for the evaluation of the parameters of cracks (their sizes and location) is based on the analysis of the nonlinearity of vibrations in the neighborhood of a superharmonic resonance of order 2/1 and/or a subharmonic resonance of order 1/2 in the case of variation of the site of application of the driving force because, as follows from the results of numerical and experimental investigations, the level of nonlinearity of the vibrations of rods with closing cracks for nonlinear resonances depends not only on the parameters of the crack but also on the site of application of the driving forces.Keywords: closing crack, sub-and superharmonic vibrations, diagnostics of the crack, nonlinear effects. Introduction.Fatigue cracks form one of the most widespread types of defects in machines and structures operating under dynamic loads. As follows from the results of numerous experimental and theoretical investigations, cracks lead to a decrease in the natural frequencies of these objects and distort the form of vibrations. The relationship between the parameters of the crack (sizes and location), on the one hand, and the changes in the natural frequencies and forms of vibrations, on the other hand, is studied in numerous works [1,2]. However, the sensitivity of the methods of diagnostics of the cracks based on the changes in the natural frequencies and forms of vibrations appeared to be to be quite low. Later, it was shown that the so-called nonlinear effects [3], i.e., the sub-and superharmonic resonances, a strong nonlinearity of vibrations at these resonances, and the characteristics of damping of vibrations, are characterized by a higher sensitivity to the presence of cracks [4].In order to simplify the analysis of nonlinear effects, it is customary to assume that the stiffness of structures suffers instantaneous changes at the times of crack closure and opening. As a rule, this phenomenon is modeled by asymmetric piecewise-linear characteristics of the restoring forces. The analytic investigations of the forced vibrations of a mechanical system with one degree of freedom and the indicated characteristic of restoring forces make it possible to reveal sub-[5-14] and superharmonic [8,9,11,13,15,16] resonances of different orders. In addition, as shown in [3,7,8], the nonlinear effects strongly depend on the dissipative properties of the investigated system: the higher the level of damping of vibrations in the system, the lower the amplitudes of nonlinear resonances and the level of nonlinearity of vibrations at these resonances.The data of experimental investigations [4,[17][18][19] demonstrate that the growth of fatigue cracks is accompanied by a significant increase in the characteristics of damping o...

Non-linearities in the vibrations of elastic structures with a closing crack: A state of the art review

“…Besides there was shown in Ref. [57] that the subharmonic mode of vibrations is extremely unstable: it may appear or disappear unexpectedly ( Fig. 7b and d).…”

“…The direct experiments [57][58][59] confirmed the existence of superharmonic resonances of order 2/1 and 4/1 and subharmonic resonance of order 1/2 of cantilever beams with a closing crack (Fig. 7).…”

“…The excitation of super-and subharmonic vibrations is possible only by reaching a certain value of the excitation force (the so-called threshold value) [47,57]. With the propagation of a fatigue crack, the threshold value decreases.…”