3-D vibration analysis of the rectangular micro damaged plates

Ahmet Kiriş; Esin İnan

doi:10.1007/978-1-4020-9100-1_21

3-D vibration analysis of the rectangular micro damaged plates

Ahmet Kiriş, Esin İnan^*

^*Corresponding author for this work

Department of Mathematics Engineering

Isik University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Citations (Scopus)

Abstract

In the present work, damaged plates are modeled by the microelongation theory which neglects the micropolar effects in Eringen’s microstretch theory. The wave propagation problem is studied and a new wave which does not appear in the classical theory of elasticity is observed. The Ritz method is extended to the microelongation theory and triplicate Chebyshev series multiplied by a boundary function are used as admissible functions to approximate plate deflection, and the frequency equations of the microelongated plate are obtained by using Chebyshev-Ritz method. The additional frequencies due to the microstructure of the plate are observed among the values of the classical frequencies. We examined the relation between these additional frequencies and the material constants of the microelongated medium and observed that these additional frequencies disappear while the all microelongational constants are taken as zero.

Original language	English
Title of host publication	8th International Conference on Vibration Problems, ICOVP 2007
Editors	Muralimohan Banerjee, Dipak Sengupta, Basudeb Mukhopadhyay, Esin Inan, Hilmi Demiray
Publisher	Springer Science and Business Media, LLC
Pages	207-214
Number of pages	8
ISBN (Print)	9781402090912
DOIs	https://doi.org/10.1007/978-1-4020-9100-1_21
Publication status	Published - 2008
Event	8th International Conference on Vibration Problems, ICOVP 2007 - Shibpur, India Duration: 1 Feb 2007 → 3 Feb 2007

Publication series

Name	Springer Proceedings in Physics
Volume	126
ISSN (Print)	0930-8989
ISSN (Electronic)	1867-4941

Conference

Conference	8th International Conference on Vibration Problems, ICOVP 2007
Country/Territory	India
City	Shibpur
Period	1/02/07 → 3/02/07

Bibliographical note

Publisher Copyright:
© Springer Science + Business Media B.V. 2008.

Keywords

Micro damaged plate
Microelongation theory
Natural frequencies

Access to Document

10.1007/978-1-4020-9100-1_21

Cite this

Kiriş, A., & İnan, E. (2008). 3-D vibration analysis of the rectangular micro damaged plates. In M. Banerjee, D. Sengupta, B. Mukhopadhyay, E. Inan, & H. Demiray (Eds.), 8th International Conference on Vibration Problems, ICOVP 2007 (pp. 207-214). (Springer Proceedings in Physics; Vol. 126). Springer Science and Business Media, LLC. https://doi.org/10.1007/978-1-4020-9100-1_21

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title = "3-D vibration analysis of the rectangular micro damaged plates",

abstract = "In the present work, damaged plates are modeled by the microelongation theory which neglects the micropolar effects in Eringen{\textquoteright}s microstretch theory. The wave propagation problem is studied and a new wave which does not appear in the classical theory of elasticity is observed. The Ritz method is extended to the microelongation theory and triplicate Chebyshev series multiplied by a boundary function are used as admissible functions to approximate plate deflection, and the frequency equations of the microelongated plate are obtained by using Chebyshev-Ritz method. The additional frequencies due to the microstructure of the plate are observed among the values of the classical frequencies. We examined the relation between these additional frequencies and the material constants of the microelongated medium and observed that these additional frequencies disappear while the all microelongational constants are taken as zero.",

keywords = "Micro damaged plate, Microelongation theory, Natural frequencies",

author = "Ahmet Kiri{\c s} and Esin İnan",

note = "Publisher Copyright: {\textcopyright} Springer Science + Business Media B.V. 2008.; 8th International Conference on Vibration Problems, ICOVP 2007 ; Conference date: 01-02-2007 Through 03-02-2007",

year = "2008",

doi = "10.1007/978-1-4020-9100-1_21",

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Kiriş, A & İnan, E 2008, 3-D vibration analysis of the rectangular micro damaged plates. in M Banerjee, D Sengupta, B Mukhopadhyay, E Inan & H Demiray (eds), 8th International Conference on Vibration Problems, ICOVP 2007. Springer Proceedings in Physics, vol. 126, Springer Science and Business Media, LLC, pp. 207-214, 8th International Conference on Vibration Problems, ICOVP 2007, Shibpur, India, 1/02/07. https://doi.org/10.1007/978-1-4020-9100-1_21

3-D vibration analysis of the rectangular micro damaged plates. / Kiriş, Ahmet; İnan, Esin.
8th International Conference on Vibration Problems, ICOVP 2007. ed. / Muralimohan Banerjee; Dipak Sengupta; Basudeb Mukhopadhyay; Esin Inan; Hilmi Demiray. Springer Science and Business Media, LLC, 2008. p. 207-214 (Springer Proceedings in Physics; Vol. 126).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Kiriş, Ahmet

AU - İnan, Esin

N1 - Publisher Copyright: © Springer Science + Business Media B.V. 2008.

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Y1 - 2008

N2 - In the present work, damaged plates are modeled by the microelongation theory which neglects the micropolar effects in Eringen’s microstretch theory. The wave propagation problem is studied and a new wave which does not appear in the classical theory of elasticity is observed. The Ritz method is extended to the microelongation theory and triplicate Chebyshev series multiplied by a boundary function are used as admissible functions to approximate plate deflection, and the frequency equations of the microelongated plate are obtained by using Chebyshev-Ritz method. The additional frequencies due to the microstructure of the plate are observed among the values of the classical frequencies. We examined the relation between these additional frequencies and the material constants of the microelongated medium and observed that these additional frequencies disappear while the all microelongational constants are taken as zero.

AB - In the present work, damaged plates are modeled by the microelongation theory which neglects the micropolar effects in Eringen’s microstretch theory. The wave propagation problem is studied and a new wave which does not appear in the classical theory of elasticity is observed. The Ritz method is extended to the microelongation theory and triplicate Chebyshev series multiplied by a boundary function are used as admissible functions to approximate plate deflection, and the frequency equations of the microelongated plate are obtained by using Chebyshev-Ritz method. The additional frequencies due to the microstructure of the plate are observed among the values of the classical frequencies. We examined the relation between these additional frequencies and the material constants of the microelongated medium and observed that these additional frequencies disappear while the all microelongational constants are taken as zero.

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ER -

3-D vibration analysis of the rectangular micro damaged plates

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Keywords

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