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

Bovsunovsky, A.; Surace, Cecilia

doi:10.1016/j.jsv.2005.01.038

Cited by 105 publications

(54 citation statements)

References 12 publications

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“…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 of vibrations for specimens made of different materials. If this increase is neglected, then the degree of damage to the vibrating system predicted on the basis of nonlinear effects is underestimated.…”

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confidence: 89%

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

Bovsunovskii

2010

Strength Mater

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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...

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confidence: 89%

“…As shown in [3,4,19,33], fatigue cracks strongly affect the damping characteristics of the specimens. Since the nonlinear effects depend on the dissipative properties of vibrating systems, special attention is given to the evaluation of the level of damping of the vibrations of cracked specimens.…”

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confidence: 99%

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

Bovsunovskii

2010

Strength Mater

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“…The analysis above shows that, since both = In mechanical engineering studies [32], the appearance of superharmonic components in the output spectrum is considered to be a significant nonlinear effect. From the perspective of the energy transfer, it is the linear FRF which transfers the input energy to the fundamental harmonic component in the output spectrum, and it is the NOFRFs which transfer the input energy to the superharmonic components.…”

Section: The Effect Of Damping On the Output Frequency Responsesmentioning

confidence: 99%

Resonances and resonant frequencies for a class of nonlinear systems

Peng

Lang

Billings

2007

Journal of Sound and Vibration

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Abstract:Resonant phenomena for a class of nonlinear systems, which can be described by a SDOF model with a polynomial type nonlinear stiffness, are investigated using Nonlinear Output Frequency Response Functions (NOFRFs). The concepts of resonance and resonant frequencies are proposed for the first time for a class of nonlinear systems.The effects of damping on the resonances and resonant frequencies are also analyzed.These results produce a novel interpretation of energy transfer phenomena in this class of nonlinear systems and show how the damping effect influences the system resonant frequencies and amplitudes. The results are important for the design and fault diagnosis of mechanical systems and structures which can be described by the SDOF nonlinear model.

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“…In mechanical engineering studies [40], the appearance of superharmonic components in the output spectrum is considered to be a significant nonlinear effect. From the perspective of the energy transfer, it is the linear FRF which transfers the input energy to the fundamental harmonic component in the output spectrum, and it is the NOFRFs which transfer the input energy to the superharmonic components.…”

Section: H J G ωmentioning

confidence: 99%

Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions

Peng

Lang

Billings

et al. 2007

International Journal of Mechanical Sciences

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In this paper, the new concept of Nonlinear Output Frequency ResponseFunctions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the Generalized Frequency Response Functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs.Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial type nonlinear oscillator, the NOFRFs are used to analyze the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model.

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

Cited by 105 publications

References 12 publications

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

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

Resonances and resonant frequencies for a class of nonlinear systems

Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions

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