The full nonlinear crack detection problem in uniform vibrating rods

Rubio, Lourdes; Fernández-Sáez, J.; Morassi, Antonino

doi:10.1016/j.jsv.2014.11.011

Cited by 16 publications

(15 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It also differs from the technique recently used by three of us in [13] in identifying a single open crack in a longitudinally vibrating beam from two resonant frequencies. The present analysis is based on a reduction of the crack identification problem to the equivalent inverse problem of determining a point mass in a simply-supported beam, and on a careful study of the eigenvalues as functions of the mass intensity and position.…”

Section: Discussionmentioning

confidence: 89%

“…Proposition 3.3 follows from the property of the zeros of the eigenfunctions of (1)- (5) (Proposition 2.1, point iv) and the definition of v given in (13).…”

Section: An Equivalent Eigenvalue Problemmentioning

confidence: 95%

“…Our method differs from that recently presented in [13] for the analysis of the analogous crack identification problem in a uniform beam under longitudinal vibration. The analysis developed in [13] was essentially based on the Frequency Equation Method, that is, a careful study of the solutions of the nonlinear system formed by the frequency equation -which is available in closed form, since the system has constant coefficients -written for the two selected resonant frequencies in terms of the position and severity of the crack.…”

mentioning

confidence: 94%

“…The analysis developed in [13] was essentially based on the Frequency Equation Method, that is, a careful study of the solutions of the nonlinear system formed by the frequency equation -which is available in closed form, since the system has constant coefficients -written for the two selected resonant frequencies in terms of the position and severity of the crack. The analysis of the corresponding nonlinear system for the cracked beam in bending turns out to be significantly more difficult, due to the simultaneous presence of harmonic ( cos ; sin ) and hyperbolic (cosh; sinh) functions.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Unique determination of a single crack in a uniform simply supported beam in bending vibration

Fernández-Sáez

Morassi

Pressacco

et al. 2016

Journal of Sound and Vibration

Self Cite

View full text Add to dashboard Cite

Section: Discussionmentioning

confidence: 89%

“…Proposition 3.3 follows from the property of the zeros of the eigenfunctions of (1)- (5) (Proposition 2.1, point iv) and the definition of v given in (13).…”

Section: An Equivalent Eigenvalue Problemmentioning

confidence: 95%

mentioning

confidence: 94%

mentioning

confidence: 99%

See 2 more Smart Citations

Unique determination of a single crack in a uniform simply supported beam in bending vibration

Fernández-Sáez

Morassi

Pressacco

et al. 2016

Journal of Sound and Vibration

Self Cite

View full text Add to dashboard Cite

“…The first result on crack identification in a longitudinally vibrating rod with a single not necessarily small crack is due to Rubio et al [28], who proved that Dilena and Morassi's result continue to hold even for large cracks, provided that the rod profile is uniform. The proof was based on a careful study of the 40 frequency equation written for the two natural frequencies used as data.…”

Section: Introductionmentioning

confidence: 99%

Crack identification in elastically restrained vibrating rods

Fernández-Sáez

Morassi

Rubio

2017

International Journal of Non-Linear Mechanics

Self Cite

View full text Add to dashboard Cite

In this paper we consider the problem of identifying an open crack in a longitudinally vibrating rod with smooth variable profile by minimal eigenfrequency data. The crack is assumed to be open during vibration and it is modelled by an elastic spring acting along the beam axis. Most, if not all, the results available in the literature for this inverse problem refer to ideal end conditions, that is the rod is either under free or supported end conditions. As an example of almost optimal result, it is known that the knowledge of the fundamental (positive) natural frequency of the rod under free-free and cantilever end conditions allows for the unique determination of the crack, without any restriction on the damage severity. In this paper we show that the analysis of the analogous crack identification problem for rods under elastically restrained end conditions leads to different results and that, in general, the knowledge of the fundamental frequency belonging to two spectra associated to different end conditions is not sufficient for the uniqueness of the solution. The method we used to solve the inverse problem is of constructive type and it is based on general properties of Preprint submitted to International Journal of Non-Linear Mechanics December 17, 2016 the eigenfrequencies as functions of the position and severity of the crack. The identification procedure has been tested numerically on rods under various damage scenarios. Numerical results agree well with the theory, even in presence of noisy input data.

show abstract