Dynamic analysis of beam with multiple cracks using Transfer Matrix Method

Nik Abdullah Nik Mohamed, Sallehuddin Mohamed Haris, Reza Alebrahim, Shakib Sharifian, Salvinder Singh Karam Singh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper studies the effect of vibration on the existing cracks in beams due to mass loading. Vibration analysis of cracked beam is one of the subjects which have attracted the attention of many researchers in this area. There are many researches that have considered crack in the beam but there are limited studies done on the beam with multiple cracks. The existence of crack in the beam cause decreasing natural frequencies which by increasing number of cracks more reduction are done. Unexpected decrease in natural frequencies toward the forced frequencies may lead the structure to failure. Vibration analysis of a beam with multiple cracks was investigated in this paper. An un-damped beam with several numbers of cracks was traversed by moving mass with constant speed. Boundary conditions were simply supported and Euler Bernoulli beam theory was considered. In order to solve the vibration analysis, Assumption Mode Method was used and then Transfer Matrix Method (TMM) was applied in order to simulate the cracked beam by calculating the natural frequencies. Maximum deflection and natural frequencies of beam for multiple numbers of cracks in different position was investigated and compared. It was concluded by increasing number of cracks in the beam maximum deflection increase while natural frequencies decrease. It was observed that for the case when the mass moves from left to right, crack attendance in the left side of the beam cause more deflection in compare with symmetrical position in the right side. By increasing number of cracks the deflection of mid-point of the beam takes longer time to reach to the maximum point which is because of the attendance of discontinuity in the beam. All results are compared with those which are available in the literature.

Original languageEnglish
Title of host publicationAdvances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012
PublisherNational Committee on Applied Mechanics
Pages1091-1098
Number of pages8
ISBN (Print)9781922107619
Publication statusPublished - 2012
Event7th Australasian Congress on Applied Mechanics, ACAM 2012 - Adelaide, SA
Duration: 9 Dec 201212 Dec 2012

Other

Other7th Australasian Congress on Applied Mechanics, ACAM 2012
CityAdelaide, SA
Period9/12/1212/12/12

Fingerprint

Transfer matrix method
Dynamic analysis
Cracks
Natural frequencies
Vibration analysis
Boundary conditions

Keywords

  • Assumption mode methods
  • Multiple cracked beams
  • Transfer matrix method

ASJC Scopus subject areas

  • Mechanics of Materials

Cite this

Nik Mohamed, N. A., Mohamed Haris, S., Alebrahim, R., Sharifian, S., & Singh, S. S. K. (2012). Dynamic analysis of beam with multiple cracks using Transfer Matrix Method. In Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012 (pp. 1091-1098). National Committee on Applied Mechanics.

Dynamic analysis of beam with multiple cracks using Transfer Matrix Method. / Nik Mohamed, Nik Abdullah; Mohamed Haris, Sallehuddin; Alebrahim, Reza; Sharifian, Shakib; Singh, Salvinder Singh Karam.

Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012. National Committee on Applied Mechanics, 2012. p. 1091-1098.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nik Mohamed, NA, Mohamed Haris, S, Alebrahim, R, Sharifian, S & Singh, SSK 2012, Dynamic analysis of beam with multiple cracks using Transfer Matrix Method. in Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012. National Committee on Applied Mechanics, pp. 1091-1098, 7th Australasian Congress on Applied Mechanics, ACAM 2012, Adelaide, SA, 9/12/12.
Nik Mohamed NA, Mohamed Haris S, Alebrahim R, Sharifian S, Singh SSK. Dynamic analysis of beam with multiple cracks using Transfer Matrix Method. In Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012. National Committee on Applied Mechanics. 2012. p. 1091-1098
Nik Mohamed, Nik Abdullah ; Mohamed Haris, Sallehuddin ; Alebrahim, Reza ; Sharifian, Shakib ; Singh, Salvinder Singh Karam. / Dynamic analysis of beam with multiple cracks using Transfer Matrix Method. Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012. National Committee on Applied Mechanics, 2012. pp. 1091-1098
@inproceedings{d5269a583a3f41af84319053e45ce9a0,
title = "Dynamic analysis of beam with multiple cracks using Transfer Matrix Method",
abstract = "This paper studies the effect of vibration on the existing cracks in beams due to mass loading. Vibration analysis of cracked beam is one of the subjects which have attracted the attention of many researchers in this area. There are many researches that have considered crack in the beam but there are limited studies done on the beam with multiple cracks. The existence of crack in the beam cause decreasing natural frequencies which by increasing number of cracks more reduction are done. Unexpected decrease in natural frequencies toward the forced frequencies may lead the structure to failure. Vibration analysis of a beam with multiple cracks was investigated in this paper. An un-damped beam with several numbers of cracks was traversed by moving mass with constant speed. Boundary conditions were simply supported and Euler Bernoulli beam theory was considered. In order to solve the vibration analysis, Assumption Mode Method was used and then Transfer Matrix Method (TMM) was applied in order to simulate the cracked beam by calculating the natural frequencies. Maximum deflection and natural frequencies of beam for multiple numbers of cracks in different position was investigated and compared. It was concluded by increasing number of cracks in the beam maximum deflection increase while natural frequencies decrease. It was observed that for the case when the mass moves from left to right, crack attendance in the left side of the beam cause more deflection in compare with symmetrical position in the right side. By increasing number of cracks the deflection of mid-point of the beam takes longer time to reach to the maximum point which is because of the attendance of discontinuity in the beam. All results are compared with those which are available in the literature.",
keywords = "Assumption mode methods, Multiple cracked beams, Transfer matrix method",
author = "{Nik Mohamed}, {Nik Abdullah} and {Mohamed Haris}, Sallehuddin and Reza Alebrahim and Shakib Sharifian and Singh, {Salvinder Singh Karam}",
year = "2012",
language = "English",
isbn = "9781922107619",
pages = "1091--1098",
booktitle = "Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012",
publisher = "National Committee on Applied Mechanics",

}

TY - GEN

T1 - Dynamic analysis of beam with multiple cracks using Transfer Matrix Method

AU - Nik Mohamed, Nik Abdullah

AU - Mohamed Haris, Sallehuddin

AU - Alebrahim, Reza

AU - Sharifian, Shakib

AU - Singh, Salvinder Singh Karam

PY - 2012

Y1 - 2012

N2 - This paper studies the effect of vibration on the existing cracks in beams due to mass loading. Vibration analysis of cracked beam is one of the subjects which have attracted the attention of many researchers in this area. There are many researches that have considered crack in the beam but there are limited studies done on the beam with multiple cracks. The existence of crack in the beam cause decreasing natural frequencies which by increasing number of cracks more reduction are done. Unexpected decrease in natural frequencies toward the forced frequencies may lead the structure to failure. Vibration analysis of a beam with multiple cracks was investigated in this paper. An un-damped beam with several numbers of cracks was traversed by moving mass with constant speed. Boundary conditions were simply supported and Euler Bernoulli beam theory was considered. In order to solve the vibration analysis, Assumption Mode Method was used and then Transfer Matrix Method (TMM) was applied in order to simulate the cracked beam by calculating the natural frequencies. Maximum deflection and natural frequencies of beam for multiple numbers of cracks in different position was investigated and compared. It was concluded by increasing number of cracks in the beam maximum deflection increase while natural frequencies decrease. It was observed that for the case when the mass moves from left to right, crack attendance in the left side of the beam cause more deflection in compare with symmetrical position in the right side. By increasing number of cracks the deflection of mid-point of the beam takes longer time to reach to the maximum point which is because of the attendance of discontinuity in the beam. All results are compared with those which are available in the literature.

AB - This paper studies the effect of vibration on the existing cracks in beams due to mass loading. Vibration analysis of cracked beam is one of the subjects which have attracted the attention of many researchers in this area. There are many researches that have considered crack in the beam but there are limited studies done on the beam with multiple cracks. The existence of crack in the beam cause decreasing natural frequencies which by increasing number of cracks more reduction are done. Unexpected decrease in natural frequencies toward the forced frequencies may lead the structure to failure. Vibration analysis of a beam with multiple cracks was investigated in this paper. An un-damped beam with several numbers of cracks was traversed by moving mass with constant speed. Boundary conditions were simply supported and Euler Bernoulli beam theory was considered. In order to solve the vibration analysis, Assumption Mode Method was used and then Transfer Matrix Method (TMM) was applied in order to simulate the cracked beam by calculating the natural frequencies. Maximum deflection and natural frequencies of beam for multiple numbers of cracks in different position was investigated and compared. It was concluded by increasing number of cracks in the beam maximum deflection increase while natural frequencies decrease. It was observed that for the case when the mass moves from left to right, crack attendance in the left side of the beam cause more deflection in compare with symmetrical position in the right side. By increasing number of cracks the deflection of mid-point of the beam takes longer time to reach to the maximum point which is because of the attendance of discontinuity in the beam. All results are compared with those which are available in the literature.

KW - Assumption mode methods

KW - Multiple cracked beams

KW - Transfer matrix method

UR - http://www.scopus.com/inward/record.url?scp=84907413034&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907413034&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84907413034

SN - 9781922107619

SP - 1091

EP - 1098

BT - Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012

PB - National Committee on Applied Mechanics

ER -