Natural frequencies of parabolic arches with a single crack on opposite cross-section sides

U. Eroglu; G. Ruta; E. Tufekci

doi:10.1177/1077546319825681

Natural frequencies of parabolic arches with a single crack on opposite cross-section sides

U. Eroglu, G. Ruta^*, E. Tufekci

^*Corresponding author for this work

Department of Mechanical Engineering

University of Rome La Sapienza

Research output: Contribution to journal › Review article › peer-review

11 Citations (Scopus)

Abstract

We study natural vibration of elastic parabolic arches, modeled as plane curved beams susceptible to elongation, shear, and bending, exhibiting small concentrated cracks. The crack is simulated by springs between regular chunks, with stiffness evaluated following stress concentration in usual crack opening modes. We evaluate and compare the linear dynamic response of the undamaged and damaged arch in nondimensional form. The governing equations are turned into a system of first-order differential equations that are solved numerically by the so-called matricant. The original contribution of this study lies in highlighting the dependence of the variation of the first natural frequencies on the crack location not only along the axis but also on opposite sides of the cross-section. We obtain the relative variations of the first frequencies in terms of the two crack locations. The result of this direct problem provides information on the possibility to detect such locations, and gives indications on structural monitoring and damage identification.

Original language	English
Pages (from-to)	1313-1325
Number of pages	13
Journal	JVC/Journal of Vibration and Control
Volume	25
Issue number	7
DOIs	https://doi.org/10.1177/1077546319825681
Publication status	Published - 1 Apr 2019

Bibliographical note

Publisher Copyright:
© The Author(s) 2019.

Funding

This work was done when U. Eroglu was Visiting Researcher at the Dipartimento d’ingegneria strutturale e geotecnica of the University of Rome ‘‘La Sapienza’’, the support of which is gratefully acknowledged. The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by The Scientific and Technological Council of Turkey (TÜBITAK) (grant number 213M608), the University of Rome ‘‘La Sapienza’’ (in 2015) (grant number C26A15JLMP), and the Italian national grant ‘‘Identification and monitoring of complex structural systems’’ (grant number PRIN 2015TTJN95).

Funders	Funder number
Scientific and Technological Council of Turkey
Foro Italico University of Rome	PRIN 2015TTJN95, C26A15JLMP
Türkiye Bilimsel ve Teknolojik Araştirma Kurumu	213M608

Keywords

Parabolic arches
localized damage
natural frequencies
two crack locations

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10.1177/1077546319825681

Cite this

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abstract = "We study natural vibration of elastic parabolic arches, modeled as plane curved beams susceptible to elongation, shear, and bending, exhibiting small concentrated cracks. The crack is simulated by springs between regular chunks, with stiffness evaluated following stress concentration in usual crack opening modes. We evaluate and compare the linear dynamic response of the undamaged and damaged arch in nondimensional form. The governing equations are turned into a system of first-order differential equations that are solved numerically by the so-called matricant. The original contribution of this study lies in highlighting the dependence of the variation of the first natural frequencies on the crack location not only along the axis but also on opposite sides of the cross-section. We obtain the relative variations of the first frequencies in terms of the two crack locations. The result of this direct problem provides information on the possibility to detect such locations, and gives indications on structural monitoring and damage identification.",

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AU - Tufekci, E.

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N2 - We study natural vibration of elastic parabolic arches, modeled as plane curved beams susceptible to elongation, shear, and bending, exhibiting small concentrated cracks. The crack is simulated by springs between regular chunks, with stiffness evaluated following stress concentration in usual crack opening modes. We evaluate and compare the linear dynamic response of the undamaged and damaged arch in nondimensional form. The governing equations are turned into a system of first-order differential equations that are solved numerically by the so-called matricant. The original contribution of this study lies in highlighting the dependence of the variation of the first natural frequencies on the crack location not only along the axis but also on opposite sides of the cross-section. We obtain the relative variations of the first frequencies in terms of the two crack locations. The result of this direct problem provides information on the possibility to detect such locations, and gives indications on structural monitoring and damage identification.

AB - We study natural vibration of elastic parabolic arches, modeled as plane curved beams susceptible to elongation, shear, and bending, exhibiting small concentrated cracks. The crack is simulated by springs between regular chunks, with stiffness evaluated following stress concentration in usual crack opening modes. We evaluate and compare the linear dynamic response of the undamaged and damaged arch in nondimensional form. The governing equations are turned into a system of first-order differential equations that are solved numerically by the so-called matricant. The original contribution of this study lies in highlighting the dependence of the variation of the first natural frequencies on the crack location not only along the axis but also on opposite sides of the cross-section. We obtain the relative variations of the first frequencies in terms of the two crack locations. The result of this direct problem provides information on the possibility to detect such locations, and gives indications on structural monitoring and damage identification.

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Natural frequencies of parabolic arches with a single crack on opposite cross-section sides

Abstract

Bibliographical note

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Keywords

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