Diagnostics of closing cracks in rodlike elements at nonlinear resonances by the method of variation of the asymmetry of driving forces

Abstract

The vibrations of elastic bodies with closing cracks are essentially nonlinear. As a specific feature of these vibrations, we can mention the manifestation of so-called nonlinear effects, in particular, sub-and superharmonic resonances and the nonlinearity of vibrations at these resonances. We propose a method for the diagnostics of cracks based on the variation of the asymmetry of driving forces. The static component of the concentrated harmonic driving force changes the state of a crack: it becomes partially or completely open or closed. Moreover, the degree of nonlinearity of vibrations for any nonlinear resonance varies from the maximum level (in the absence of static component) to its almost complete absence in the case where the crack becomes open or closed in the course of vibrations under the action of the static component. The proposed method enables one to detect the presence of cracks without any preliminary data on the analyzed object in the intact state.Keywords: closing crack, sub-and superharmonic vibrations, diagnostics of cracks, nonlinear effects, asymmetry of the driving force.Introduction. The problem of detection of the cracks of subcritical sizes with an aim of prevention of the failures of machines and structures of different kinds is one of the most urgent problems of engineering diagnostics. The last decades were marked by the rapid development of the vibration methods of diagnostics of defects based, as a rule, on the analysis of the changes in the natural frequencies of vibrations and distortions of their shapes caused by the cracks [1, 2]. However, the sensitivity of these methods proved to be insufficient for practical application. Higher sensitivities to the presence of cracks are exhibited by the so-called nonlinear effects [3], i.e., sub-and superharmonic resonances, and the well-pronounced nonlinearity of vibrations at these resonances.In the case of vibration of a body containing a crack, the events of crack opening and closure are accompanied by the variations of stiffness of the entire structure simulated, for the sake of simplicity, by an asymmetric piecewise linear characteristic of the restoring force. The analytic investigations of forced vibrations of the mechanical systems with one degree of freedom and the indicated characteristic of the restoring force reveal the possibility of appearance of sub-[4-13] and superharmonic [7,8,10,12,14,15] resonance vibrations of various orders. Similar results were also obtained in the numerical investigations of the forced vibrations of rods with closing cracks [10,[16][17][18].The idea of modeling of the process of vibrations in cracked structural elements subjected to the action of static forces was realized by analyzing free [19,20] and forced [21] vibrations of rods. These investigations were carried out due to the necessity of more exact analysis of the conditions of loading of structural elements either operating in the fields of significant centrifugal forces (e.g., blades of gas-turbine engines) or carrying large static loads ...

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

“…The weight can determine the static deformation of a structure which causes crack to open or close partially or fully [38,60,61] making non-linear effects useless for crack detection. To avoid this problem Tsyfansky and Beresnevich [60], who investigated a model of an aircraft wing, applied an additional static force component to compensate the weight of the structure.…”

“…On the other hand, the change of the non-linearity level in the vibration response at super-or subharmonic resonances due to the variation of the static component in the harmonic driving force signal may serve as an indicator of crack presence [61]. and subharmonic resonance of order 1/2 is strongly dependent on the driving force application point (L p ).…”

Damages Identification in the Cantilever-based on the Parameters of the Natural Oscillations

“…Solving the problem of identification of damage in rods, beams and more complex structures analysis of these studies is described in reviews [1][2][3][4][5][6][7][8][9] . Studies investigating problems of parameter identification of damages and their location in the structural elements have been conducted using a variety of analytical and finite element models 10 , combined c using artificial neural networks 11,12 , as well as the base of field experiments using a strain gauge, optical and vibrodiagnostic techniques 13,14 .…”

Approximate analytical method for determining the vibration-diagnostic parameter indicating the presence of a crack in a distributed-parameter elastic system at super- and subharmonic resonances

“…In view of the complexity of the analytical solution of problems of this kind and the finding of constitutive equations that are convenient for calculation, the numerical solutions are usually applied using the finite element model of an elastic body [3][4][5][6][7][8][9]. Sometimes, the electric analog modeling of the derived set of finite difference equations approximating, for example, the differential equation for the bending vibration of a rod element with the given law of mass distribution and bending rigidity of the section is employed [10,11].…”