Skip to main content
Erschienen in: Strength of Materials 2/2022

13.06.2022

Determination of the Effect of a Mode I Surface Crack Cross-Sectional Shape on the Characteristics of the Forced Bending Vibrations of a Cantilever Beam

verfasst von: E. O. Onyshchenko, A. P. Zinkovskii, V. V. Matveev

Erschienen in: Strength of Materials | Ausgabe 2/2022

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The results of computational experiments for determining the effect of a mode I surface fatigue crack cross-sectional shape in a rectangular cantilever beam on the characteristics of its free and forced bending vibrations with varying cross-sectional dimensions of the crack and its longitudinal position are presented. Finite-element models of beams with 8-node 3D finite elements were developed for carrying out investigations. Three types of a breathing crack cross-section were considered: rectangular, triangular, and trapezoidal one, with the solution of a contact problem to ensure the non-penetration of crack edges. Plots of relative change in the natural frequency of vibration, the amplitudes of the first and second harmonics and their ratios at the main, super- and subharmonic resonances versus the shape, relative area and location of the crack were obtained. It is shown that when bending vibrations of the beam with a rectangular crack, are excited along the axis Oy, there arise displacements only in the direction of driving force, while in the case of triangular and trapezoidal cracks, there arise additional displacements along the axis of minimum stiffness, Oz. It was found that the change in the natural frequency of the beam, as well as the ratio of the amplitudes of dominant harmonics during the recording of vibrations along the excitation axis at the main, super- and subharmonic resonances increase with increasing relative area of the crack cross-section. Under this condition, their largest value was characteristic of a rectangular crack, and the smallest of a triangular one. It was noted that a characteristic indicator of the asymmetric shape of the crack was the appearance of vibrations in the plane perpendicular to the excitation plane.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat B. Panigrahi and G. Pohit, “Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach,” P. I. Mech. Eng. C-J. Mec., 230, No. 9, 1486–1497 (2016).CrossRef B. Panigrahi and G. Pohit, “Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach,” P. I. Mech. Eng. C-J. Mec., 230, No. 9, 1486–1497 (2016).CrossRef
2.
Zurück zum Zitat A. C. Neves, F. M. F. Simoes, and A. Pinto da Costa, “Vibrations of cracked beams: Discrete mass and stiffness models,” Comput. Struct., 168, 68–77 (2016).CrossRef A. C. Neves, F. M. F. Simoes, and A. Pinto da Costa, “Vibrations of cracked beams: Discrete mass and stiffness models,” Comput. Struct., 168, 68–77 (2016).CrossRef
3.
4.
Zurück zum Zitat R. O. Curadelli, J. D. Riera, D. Ambrosini, and M. G. Amania, “Damage detection by means of structural damping identification,” Eng. Struct., 30, 3497–3504 (2008).CrossRef R. O. Curadelli, J. D. Riera, D. Ambrosini, and M. G. Amania, “Damage detection by means of structural damping identification,” Eng. Struct., 30, 3497–3504 (2008).CrossRef
5.
Zurück zum Zitat E. Asnaashari and J. K. Sinha, “Development of residual operational deflection shape for crack detection in structures,” Mech. Syst. Signal Pr., 43, 113–123 (2014).CrossRef E. Asnaashari and J. K. Sinha, “Development of residual operational deflection shape for crack detection in structures,” Mech. Syst. Signal Pr., 43, 113–123 (2014).CrossRef
6.
Zurück zum Zitat P. E. Cooley, J. C. Slater, and O. V. Shiryayev, “Investigation of a vibration-based damage identification technique for breathing fatigue cracks,” in: Proc. of the 56th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf. (Kissimmee, Florida, USA) (2015), https://doi.org/https://doi.org/10.2514/6.2015-0693. P. E. Cooley, J. C. Slater, and O. V. Shiryayev, “Investigation of a vibration-based damage identification technique for breathing fatigue cracks,” in: Proc. of the 56th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf. (Kissimmee, Florida, USA) (2015), https://​doi.​org/​https://​doi.​org/​10.​2514/​6.​2015-0693.
7.
Zurück zum Zitat W. Zhang, H. Ma, J. Zeng, et al., “Vibration responses analysis of an elastic-support cantilever beam with crack and offset boundary,” Mech. Syst. Signal Pr., 95, 205–218 (2017).CrossRef W. Zhang, H. Ma, J. Zeng, et al., “Vibration responses analysis of an elastic-support cantilever beam with crack and offset boundary,” Mech. Syst. Signal Pr., 95, 205–218 (2017).CrossRef
8.
Zurück zum Zitat E. A. Sinenko and A. P. Zinkovskii, “Influence of the exciting force application point on the amplitude spectrum of flexural vibrations in a beam with a “breathing” crack,” Strength Mater., 47, No. 4, 553–560 (2015), https://doi.org/https://doi.org/10.1007/s11223-015-9689-0. E. A. Sinenko and A. P. Zinkovskii, “Influence of the exciting force application point on the amplitude spectrum of flexural vibrations in a beam with a “breathing” crack,” Strength Mater., 47, No. 4, 553–560 (2015), https://​doi.​org/​https://​doi.​org/​10.​1007/​s11223-015-9689-0.
9.
Zurück zum Zitat V. V. Matveev, A. P. Yakovlev, O. E. Boginich, and E. A. Sinenko, “Approximate analytical determination parameters of vibrodiagnostic parameters of the presence of a closing crack in bar elements under subharmonic resonance,” Strength Mater., 46, No. 3, 315–237 (2014), https://doi.org/https://doi.org/10.1007/s11223-014-9553-7. V. V. Matveev, A. P. Yakovlev, O. E. Boginich, and E. A. Sinenko, “Approximate analytical determination parameters of vibrodiagnostic parameters of the presence of a closing crack in bar elements under subharmonic resonance,” Strength Mater., 46, No. 3, 315–237 (2014), https://​doi.​org/​https://​doi.​org/​10.​1007/​s11223-014-9553-7.
10.
Zurück zum Zitat V. V. Matveev, O. E. Boginich, E. A. Sinenko, and A. P. Yakovlev, “On vibrodiagnostics of the presence of a closing edge crack in a beam with amplitude-dependent damping capacity under superharmonic resonance,” Strength Mater., 47, No. 5, 653–661 (2015), https://doi.org/https://doi.org/10.1007/s11223-015-9701-8. V. V. Matveev, O. E. Boginich, E. A. Sinenko, and A. P. Yakovlev, “On vibrodiagnostics of the presence of a closing edge crack in a beam with amplitude-dependent damping capacity under superharmonic resonance,” Strength Mater., 47, No. 5, 653–661 (2015), https://​doi.​org/​https://​doi.​org/​10.​1007/​s11223-015-9701-8.
11.
Zurück zum Zitat J. Zeng, H. Ma, W. Zhang, and B. Wen, “Dynamic characteristic analysis of cracked cantilever beams under different crack types,” Eng. Fail. Anal., 74, 80–94 (2017).CrossRef J. Zeng, H. Ma, W. Zhang, and B. Wen, “Dynamic characteristic analysis of cracked cantilever beams under different crack types,” Eng. Fail. Anal., 74, 80–94 (2017).CrossRef
12.
Zurück zum Zitat A. Bouboulas and N. Anifantis, “Three-dimensional finite element modeling for post-buckling analysis of cracked columns,” Int. J. Struct. Integr., 7, No. 3, 397–411 (2016).CrossRef A. Bouboulas and N. Anifantis, “Three-dimensional finite element modeling for post-buckling analysis of cracked columns,” Int. J. Struct. Integr., 7, No. 3, 397–411 (2016).CrossRef
13.
Zurück zum Zitat T. Y. Kam and T. Y. Lee, “Detection of cracks in structures using modal test data,” Eng. Fract. Mech., 42, No. 2, 381–387 (1997).CrossRef T. Y. Kam and T. Y. Lee, “Detection of cracks in structures using modal test data,” Eng. Fract. Mech., 42, No. 2, 381–387 (1997).CrossRef
14.
Zurück zum Zitat Y. S. Lee and M. J. Chung, “A study on crack detection using eigenfrequency test data,” Comput. Struct., 77, 327–342 (2000).CrossRef Y. S. Lee and M. J. Chung, “A study on crack detection using eigenfrequency test data,” Comput. Struct., 77, 327–342 (2000).CrossRef
15.
Zurück zum Zitat H. Long, Y. L. Liu, and K. F. Liu, “Nonlinear vibration analysis of a beam with a breathing crack,” Appl. Sci., 9, 1–17 (2019). H. Long, Y. L. Liu, and K. F. Liu, “Nonlinear vibration analysis of a beam with a breathing crack,” Appl. Sci., 9, 1–17 (2019).
16.
Zurück zum Zitat J. Liu, Y. Shao, and W. Zhu, “Free vibration analysis of a cantilever boam with a slant edge crack,” P. I. Mech. Eng. C-J. Mec., 231, No. 5, 823–843 (2017).CrossRef J. Liu, Y. Shao, and W. Zhu, “Free vibration analysis of a cantilever boam with a slant edge crack,” P. I. Mech. Eng. C-J. Mec., 231, No. 5, 823–843 (2017).CrossRef
17.
Zurück zum Zitat A. P. Zinkovskii and I. G. Tokar’, “Influence of local surface damage on the natural frequencies of the higher modes of flexural vibration of cantilever rods,” Strength Mater., 50, No. 4, 557–564 (2018), https://doi.org/https://doi.org/10.1007/s11223-018-0001-y. A. P. Zinkovskii and I. G. Tokar’, “Influence of local surface damage on the natural frequencies of the higher modes of flexural vibration of cantilever rods,” Strength Mater., 50, No. 4, 557–564 (2018), https://​doi.​org/​https://​doi.​org/​10.​1007/​s11223-018-0001-y.
18.
Zurück zum Zitat U. Andreaus, P. Casini, and F. Vestroni, “Nonlinear features in the dynamic response of a cracked beam under harmonic forcing,” in: Proc. of the 2005 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Sept. 24–28, 2005, Long Beach, CA, USA), Vol. 6C, DETC2005-85672, ASME (2005), pp. 2083–2089. U. Andreaus, P. Casini, and F. Vestroni, “Nonlinear features in the dynamic response of a cracked beam under harmonic forcing,” in: Proc. of the 2005 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Sept. 24–28, 2005, Long Beach, CA, USA), Vol. 6C, DETC2005-85672, ASME (2005), pp. 2083–2089.
19.
Zurück zum Zitat U. Andreaus, P. Casini, and F. Vestroni, “Non-linear dynamics of a cracked cantilever beam under harmonic excitation,” Int. J. Nonlin. Mech., 42, 566–575 (2007).CrossRef U. Andreaus, P. Casini, and F. Vestroni, “Non-linear dynamics of a cracked cantilever beam under harmonic excitation,” Int. J. Nonlin. Mech., 42, 566–575 (2007).CrossRef
20.
Zurück zum Zitat N. M. Newmark, “A method of computation for structural dynamics,” J. Eng. Mech. Div.-ASCE, 85, 67–94 (1959).CrossRef N. M. Newmark, “A method of computation for structural dynamics,” J. Eng. Mech. Div.-ASCE, 85, 67–94 (1959).CrossRef
21.
Zurück zum Zitat O. Giannini, P. Casini, and F. Vestroni, “Nonlinear harmonic identification of breathing cracks in beams,” Comput. Struct., 129, 166–177 (2013).CrossRef O. Giannini, P. Casini, and F. Vestroni, “Nonlinear harmonic identification of breathing cracks in beams,” Comput. Struct., 129, 166–177 (2013).CrossRef
Metadaten
Titel
Determination of the Effect of a Mode I Surface Crack Cross-Sectional Shape on the Characteristics of the Forced Bending Vibrations of a Cantilever Beam
verfasst von
E. O. Onyshchenko
A. P. Zinkovskii
V. V. Matveev
Publikationsdatum
13.06.2022
Verlag
Springer US
Erschienen in
Strength of Materials / Ausgabe 2/2022
Print ISSN: 0039-2316
Elektronische ISSN: 1573-9325
DOI
https://doi.org/10.1007/s11223-022-00393-4

Weitere Artikel der Ausgabe 2/2022

Strength of Materials 2/2022 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.