Non-Linear Vibration Method for Detection of Fatigue Cracks in Aircraft Wings

Tsyfansky, S.L.; Beresnevich, Vitaly

doi:10.1006/jsvi.2000.2981

Cited by 81 publications

(34 citation statements)

References 8 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They noted some nonlinear features of the spectra; they in fact observed a modest crack signature from a crack halfway through the thickness of a simply supported beam. More recently, researchers have been looking at the steady state response of the beam to a single harmonic input while including the non linear effects of crack closure and outlining procedures of sub-and super-resonant diagnostics [7].…”

Section: Introductionmentioning

confidence: 99%

Non-linear dynamics of a cracked cantilever beam under harmonic excitation

Andreaus¹,

Casini²,

Vestroni³

2007

International Journal of Non-Linear Mechanics

190

View full text Add to dashboard Cite

The presence of cracks in a structure is usually detected by adopting a linear approach through the monitoring of changes in its dynamic response features, such as natural frequencies and mode shapes. The problem of a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite elements; the behaviour of the breathing crack is simulated as a frictionless contact problem. The modification of the response with respect to the linear one is outlined: in particular, excitation of sub-and super-harmonics, period doubling, quasi-impulsive behaviour at crack interfaces are the main achievements. These response characteristics, strictly due to the presence of a crack, can be used in nonlinear techniques of crack identification.

show abstract

Section: Introductionmentioning

confidence: 99%

Non-linear dynamics of a cracked cantilever beam under harmonic excitation

Andreaus¹,

Casini²,

Vestroni³

2007

International Journal of Non-Linear Mechanics

190

View full text Add to dashboard Cite

show abstract

“…They also observed antiresonance frequency shifts and super/subharmonic vibration phenomena in the experimental study of naturally grown fatigue cracks. It was also observed in the bending vibration encountered in an aircraft wing under external harmonic excitation [18] that elastic nonlinearity of crack results in the generation of superharmonic vibration regimes. In [19], nonlinear systems of algebraic equations were defined to model the cantilever beam with several breathing cracks to study the vibration response.…”

Section: Introductionmentioning

confidence: 86%

On the modelling of dynamic structures with discontinuities

2011

View full text Add to dashboard Cite

A method of simulation is developed for studying the dynamics of the structures with discontinuities using Matlab-Simulink. The concept of dynamic compliance is used for modeling the continuous elements of the structure and the local discontinuity is modeled as nonlinear feedback. As an example, a one-dimensional model of cracked bar under harmonic loading is considered for the simulation purpose.

show abstract

“…3). Some adjustment occurs due to the nonlinear dependence À 2 on the ratio of the parameter a d [see formulas (13)]. …”

mentioning

confidence: 99%

“…For the considered case of excitation of vibrations of a hinge-supported rod, the difference between the data calculation by formulas (27) and (29) . for x l c = 0.1, 0.25, and 0.5, their corresponding values of the nonlinearity parameter of the vibration process À 2 for the vibration decrement d = 0.01 were calculated using formulas (27) and (29), (30) and relationships (13). For convenience of the further analysis, the dependences of the relative acceleration amplitude of the second harmonic À à 2 on the point of application of the driving force for the cases of different locations of the crack x l c are presented in Fig.…”

mentioning

confidence: 99%

“…A periodic change in the bending rigidity of the cracked section during its opening/closure is simulated by the change in the corresponding capacitor in the electrical model is carried out with the help of a nonlinear unit. Based on the obtained results, the vibration-diagnostic method of searching for fatigue cracks in wings of airborne vehicles was proposed [12,13].…”

mentioning

confidence: 99%

See 1 more Smart Citation

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

2010

View full text Add to dashboard Cite

620.178.5:620.179 and A. P. YakovlevAn approximate method for calculating the vibration-diagnostic parameter indicating the presence of a crack in an elastic distributed-parameter system at super-and subharmonic resonances is considered. The method involves the finding of the non-linearity characteristic of an elastic system based on the analysis of its forced vibrations in the undamaged state and the use of results of the approximate analytical determination of parameters of nonlinearity for vibrations of an elastic body with a closing crack, which is simulated by a single-degree-of-freedom system with an asymmetric bilinear characteristic of the restoring force at the above-mentioned resonances.Keywords: super-and subharmonic resonances, vibration-based diagnostics of fatigue damage, closing crack, nonlinear vibrations, distributed-parameter elastic system. Introduction.Interest in studying vibrations of elastic bodies in the presence of damages such as fatigue cracks is motivated by the necessity of evaluating a possible change in the vibrational state of structural elements during their operation on the one hand, and by the development of the efficient methods of vibration-based diagnostics of this kind of damages, on the other. Here, one of the most investigated lines of research is establishing the calculated relationships between the parameters of the closing Mode I crack and vibration process at super-and subharmonic resonances. This is due to the complexity of the analytical solution of the problem on forced vibrations of a substantially nonlinear system derived.In this field, a number of investigations are known. Thus, in [1], the problem of transverse oscillations of a prismatic beam with a closing crack at subharmonic 2-nd order resonance under the action of a harmonic transverse concentrated load was considered using the Ostrogradsky-Hamilton principle and Ritz method. The weakening of the bending rigidity of the girder with an open crack was interpreted as a local decrease in the effective cross section of the beam in the limited region approximated by a triangular prism having a right angle at the crack tip and a height equal to the crack depth. It was assumed that in the region of the resonance, the beam performs vibrations close to one of the natural modes, and the mathematical model of such vibrations was represented by one ordinary differential equation in which the sign of the term corresponding to the so-called reduced depth of the crack was governed by the sign of the quasi-normal coordinate. Next, using the averaging method, the set of the time-independent differential equations was set up for determining the amplitude and phase of the second harmonic of the vibration process.The problem on forced vibrations of a rectangular plate containing longitudinal defects of continuity, such as closing cracks, was considered in [2] for the case of superharmonic second-order resonance of the first mode of transverse vibration. To solve it, the Ostrogradsky-Hamilton principle and Ritz method were a...

show abstract

Non-Linear Vibration Method for Detection of Fatigue Cracks in Aircraft Wings

Cited by 81 publications

References 8 publications

Non-linear dynamics of a cracked cantilever beam under harmonic excitation

Non-linear dynamics of a cracked cantilever beam under harmonic excitation

On the modelling of dynamic structures with discontinuities

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

Contact Info

Product

Resources

About