Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics

Andris Freimanis; Ainars Paeglitis

doi:10.1007/978-3-319-74700-2_41

Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics

Andris Freimanis^*
, Ainars Paeglitis

^*Corresponding author for this work

Not published at VTT

Riga Technical University

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

2 Citations (Scopus)

Abstract

Modal analysis is widely used to validate numerical models, for quality control in manufacturing, and to detect structural damage. However, it is hard to compute modes of a structure with cracks, because the partial differential equations used in continuum mechanics are undefined along discontinuities in the deformation field. Peridynamic theory is a nonlocal extension of continuum mechanics that uses integral equations, which are defined in presence of cracks. Therefore, it is can be used to analyze changes in natural frequencies and mode shapes due to cracking. In this study, we compute the first five modes of 3D isotropic plates made from poly(methyl methacrylate) with free-free boundary conditions in peridynamics and compare them to experimental and finite-element analysis results. Afterwards, we introduce a crack in the cross-section and again compare the peridynamic and experimental results. Peridynamic natural frequencies of both healthy and cracked plates are within 3% of the experimental results and show similar frequency shifts due to damage. PD mode shapes match the experimental ones in both healthy and cracked cases.

Original language	English
Title of host publication	Topics in Modal Analysis & Testing
Subtitle of host publication	Proceedings of 36th IMAC, A Conference and Exposition on Structural Dynamics 2018
Editors	Michael Mains, Brandon J. Dilworth
Publisher	Taylor & Francis
Pages	359-361
Volume	9
ISBN (Print)	978-3-319-74699-9, 978-3-319-74700-2
DOIs	https://doi.org/10.1007/978-3-319-74700-2_41
Publication status	Published - 2019
MoE publication type	A4 Article in a conference publication
Event	36th IMAC, A Conference and Exposition on Structural Dynamics 2018 - Orlando, United States Duration: 12 Feb 2018 → 15 Feb 2018

Publication series

Series	Conference Proceedings of the Society for Experimental Mechanics Series
ISSN	2191-5644

Conference

Conference	36th IMAC, A Conference and Exposition on Structural Dynamics 2018
Country/Territory	United States
City	Orlando
Period	12/02/18 → 15/02/18

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 9 Industry, Innovation, and Infrastructure

Keywords

Crack
Damage
Eigenvalues
Modal analysis
Peridynamics

Access to Document

10.1007/978-3-319-74700-2_41

Cite this

Freimanis, Andris ; Paeglitis, Ainars. / Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics. Topics in Modal Analysis & Testing: Proceedings of 36th IMAC, A Conference and Exposition on Structural Dynamics 2018. editor / Michael Mains ; Brandon J. Dilworth. Vol. 9 Taylor & Francis, 2019. pp. 359-361 (Conference Proceedings of the Society for Experimental Mechanics Series).

@inproceedings{1d0df3c913354b669eed090657840f3c,

title = "Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics",

abstract = "Modal analysis is widely used to validate numerical models, for quality control in manufacturing, and to detect structural damage. However, it is hard to compute modes of a structure with cracks, because the partial differential equations used in continuum mechanics are undefined along discontinuities in the deformation field. Peridynamic theory is a nonlocal extension of continuum mechanics that uses integral equations, which are defined in presence of cracks. Therefore, it is can be used to analyze changes in natural frequencies and mode shapes due to cracking. In this study, we compute the first five modes of 3D isotropic plates made from poly(methyl methacrylate) with free-free boundary conditions in peridynamics and compare them to experimental and finite-element analysis results. Afterwards, we introduce a crack in the cross-section and again compare the peridynamic and experimental results. Peridynamic natural frequencies of both healthy and cracked plates are within 3\% of the experimental results and show similar frequency shifts due to damage. PD mode shapes match the experimental ones in both healthy and cracked cases.",

keywords = "Crack, Damage, Eigenvalues, Modal analysis, Peridynamics",

author = "Andris Freimanis and Ainars Paeglitis",

note = "Publisher Copyright: {\textcopyright} The Society for Experimental Mechanics, Inc. 2019.; 36th IMAC, A Conference and Exposition on Structural Dynamics 2018 ; Conference date: 12-02-2018 Through 15-02-2018",

year = "2019",

doi = "10.1007/978-3-319-74700-2\_41",

language = "English",

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series = "Conference Proceedings of the Society for Experimental Mechanics Series",

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booktitle = "Topics in Modal Analysis \& Testing",

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}

Freimanis, A & Paeglitis, A 2019, Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics. in M Mains & BJ Dilworth (eds), Topics in Modal Analysis & Testing: Proceedings of 36th IMAC, A Conference and Exposition on Structural Dynamics 2018. vol. 9, Taylor & Francis, Conference Proceedings of the Society for Experimental Mechanics Series, pp. 359-361, 36th IMAC, A Conference and Exposition on Structural Dynamics 2018, Orlando, Florida, United States, 12/02/18. https://doi.org/10.1007/978-3-319-74700-2_41

Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics. / Freimanis, Andris; Paeglitis, Ainars.
Topics in Modal Analysis & Testing: Proceedings of 36th IMAC, A Conference and Exposition on Structural Dynamics 2018. ed. / Michael Mains; Brandon J. Dilworth. Vol. 9 Taylor & Francis, 2019. p. 359-361 (Conference Proceedings of the Society for Experimental Mechanics Series).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics

AU - Freimanis, Andris

AU - Paeglitis, Ainars

N1 - Publisher Copyright: © The Society for Experimental Mechanics, Inc. 2019.

PY - 2019

Y1 - 2019

N2 - Modal analysis is widely used to validate numerical models, for quality control in manufacturing, and to detect structural damage. However, it is hard to compute modes of a structure with cracks, because the partial differential equations used in continuum mechanics are undefined along discontinuities in the deformation field. Peridynamic theory is a nonlocal extension of continuum mechanics that uses integral equations, which are defined in presence of cracks. Therefore, it is can be used to analyze changes in natural frequencies and mode shapes due to cracking. In this study, we compute the first five modes of 3D isotropic plates made from poly(methyl methacrylate) with free-free boundary conditions in peridynamics and compare them to experimental and finite-element analysis results. Afterwards, we introduce a crack in the cross-section and again compare the peridynamic and experimental results. Peridynamic natural frequencies of both healthy and cracked plates are within 3% of the experimental results and show similar frequency shifts due to damage. PD mode shapes match the experimental ones in both healthy and cracked cases.

AB - Modal analysis is widely used to validate numerical models, for quality control in manufacturing, and to detect structural damage. However, it is hard to compute modes of a structure with cracks, because the partial differential equations used in continuum mechanics are undefined along discontinuities in the deformation field. Peridynamic theory is a nonlocal extension of continuum mechanics that uses integral equations, which are defined in presence of cracks. Therefore, it is can be used to analyze changes in natural frequencies and mode shapes due to cracking. In this study, we compute the first five modes of 3D isotropic plates made from poly(methyl methacrylate) with free-free boundary conditions in peridynamics and compare them to experimental and finite-element analysis results. Afterwards, we introduce a crack in the cross-section and again compare the peridynamic and experimental results. Peridynamic natural frequencies of both healthy and cracked plates are within 3% of the experimental results and show similar frequency shifts due to damage. PD mode shapes match the experimental ones in both healthy and cracked cases.

KW - Crack

KW - Damage

KW - Eigenvalues

KW - Modal analysis

KW - Peridynamics

UR - https://www.scopus.com/pages/publications/85061379104

U2 - 10.1007/978-3-319-74700-2_41

DO - 10.1007/978-3-319-74700-2_41

M3 - Conference article in proceedings

SN - 978-3-319-74699-9

SN - 978-3-319-74700-2

VL - 9

T3 - Conference Proceedings of the Society for Experimental Mechanics Series

SP - 359

EP - 361

BT - Topics in Modal Analysis & Testing

A2 - Mains, Michael

A2 - Dilworth, Brandon J.

PB - Taylor & Francis

T2 - 36th IMAC, A Conference and Exposition on Structural Dynamics 2018

Y2 - 12 February 2018 through 15 February 2018

ER -

Freimanis A, Paeglitis A. Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics. In Mains M, Dilworth BJ, editors, Topics in Modal Analysis & Testing: Proceedings of 36th IMAC, A Conference and Exposition on Structural Dynamics 2018. Vol. 9. Taylor & Francis. 2019. p. 359-361. (Conference Proceedings of the Society for Experimental Mechanics Series). doi: 10.1007/978-3-319-74700-2_41

Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics

Abstract

Publication series

Conference

UN SDGs

Keywords

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