Natural frequencies of a bar with multiple cracks

Ruotolo, Romualdo; Surace, Cecilia

doi:10.1016/s0022-460x(03)00761-2

Cited by 53 publications

(32 citation statements)

References 23 publications

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“…This is a new form of the frequency equation in axial vibration for multiple cracked bar [2]. Obviously, the latter equation is determined by the determinant of order identical to the number of cracks.…”

Section: Summarized Theoretical Aspectsmentioning

confidence: 98%

Change in mode shape nodes of multiple cracked bar: II. The numerical analysis

Khiem¹,

Toan²,

Khue³

2013

Vietnam J. Mech.

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Section: Summarized Theoretical Aspectsmentioning

confidence: 98%

Change in mode shape nodes of multiple cracked bar: II. The numerical analysis

Khiem¹,

Toan²,

Khue³

2013

Vietnam J. Mech.

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“…Haisty and Springer 1988;Ostachowicz and Krawczuk 1991;Patil and Maiti 2003;Ruotolo, and Surace 2004). These relations are based on fracture mechanics.…”

Section: Spring Stiffness-crack Relationmentioning

confidence: 99%

“…For open crack with total depth δ under axial loading, the axial spring stiffness expression is given by Ruotolo and Surace (2004): …”

Section: Latin American Journal Of Solids and Structures 13 (2016) 16mentioning

confidence: 99%

“…Crack detection in bars, rods and shafts is particularly important as they are used in all rotating machines and gearboxes, and may lead to tragic accidents (Samuel and Pines 2005). Ruotolo and Surace (2004) derived expressions for the natural frequencies of bars with multiple cracks. Chondros et al (1997Chondros et al ( , 1998 derived the governing differential equation of a cracked bar.…”

Section: Introductionmentioning

confidence: 99%

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Crack Detection Using Mixed Axial and Bending Natural Frequencies in Metallic Euler-Bernoulli Beam

Mostafa

Tawfik

2016

Lat. Am. j. solids struct.

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For many years, several crack detection attempts have been using measurements of the structure's modal parameters. One of the easiest is to measure and correlate the change in natural frequencies to cracks. The direct and inverse problem have been discussed in literature. However, the inverse problem, being addressed in this paper, is a challenging one, where it starts by measuring certain structural properties and estimate the corresponding crack location and size. Unlike previous studies that utilizing natural frequencies from one direction, both axial and bending natural frequencies are used together to determine crack size and location, without prior estimation of natural frequencies of the intact beam. The results obtained showing promising capabilities in crack detection.

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“…h is the crack ratio; see, for example, Ruotolo and Surace (2004 Table 4. Natural frequencies and antiresonances are obtained by solving the direct eigenvalue problem exactly in undamaged and damaged conditions.…”

Section: Applicationsmentioning

confidence: 99%

Identification of two cracks with different severity in beams and rods from minimal frequency data

Rubio

Fernández-Sáez

Morassi

2014

Journal of Vibration and Control

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It has been known for a long time that the problem of identifying two small cracks in a simply supported beam from the first three natural frequencies can be analytically formulated and solved if the two cracks have equal severity. In this paper we extend this result to the case of cracks with different severity. Each crack is simulated by a rotational elastic spring and the inverse problem is solved in terms of the damage-induced changes in the first four natural frequencies. Closed-form expressions of the damage parameters in terms of the measured frequencies are obtained. The results can be extended to the identification of two cracks in a longitudinally vibrating beam based on a suitable set of natural frequency and antiresonant frequency data. Numerical simulations support the theory, and show that if accurate input data are available and the cracks are not too close, then damage identification leads to satisfactory results.

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Natural frequencies of a bar with multiple cracks

Cited by 53 publications

References 23 publications

Change in mode shape nodes of multiple cracked bar: II. The numerical analysis

Change in mode shape nodes of multiple cracked bar: II. The numerical analysis

Crack Detection Using Mixed Axial and Bending Natural Frequencies in Metallic Euler-Bernoulli Beam

Identification of two cracks with different severity in beams and rods from minimal frequency data

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