Research Article
Sonlu elemanlar yöntemi ile çatlaklı konik kirişlerde serbest titreşim analizi ve hasar konumlarının belirlenmesi
Abstract
Bu çalışmada, hasarlı konik kirişlerin serbest titreşim analizleri için iki düğüm noktalı ve her bir düğüm noktasında dörder serbestliği (yatay ve düşey ötelenme, dönme ve eğrilik) bulunan bir sonlu eleman modeli sunulmuştur. Değişken kesitli Bernoulli-Euler kirişi için rijitlik ve kütle matrisleri Galerkin yöntemi ile elde edilmiştir. Sonlu eleman formülasyonunda, uzama titreşimleri için doğrusal Lagrange, eğilme titreşimleri için ise beşinci dereceden Hermit polinomları seçilmiştir. Hasarın tanımlanması için eleman rijitlik matrisi bir rijitlik kaybı katsayısı ile çarpılmıştır. Hasar sebebiyle eleman kütle matrisinde değişim olmadığı kabul edilmiştir. Önerilen elemanın doğruluğu, literatürdeki çalışmalarla karşılaştırmalar yapılarak gösterilmiştir. Modal eğrilik değişiminin hasar (çatlak) konumlarının bulunmasındaki başarısını göstermek amacıyla bazı sayısal sonuçlar sunulmuştur.
References
- [1] Salawu O.S., Detection of structural damage through changes in frequency: A review, Eng Struct, 19, 718–723, 1997.
- [2] Doebling S.W., Farrar C.R., Prime M.B., A summary review of vibration-based damage identification methods, Shock Vib Dig, 30, 91–105, 1998.
- [3] Sinou J.J., A Review of Damage Detection and Health Monitoring of Mechanical Systems from Changes in the Measurement of Linear and Non-Linear Vibrations, Mechanical Vibrations: Measurements, Effects and Control, Editor: Sapri R.C., Nova Science Publishers, Inc., 643–702, 2009.
- [4] Farrar C.R., Worden K., An introduction to structural health monitoring, CISM International Centre for Mechanical Sciences, Courses and Lectures, 365(1851), 303–315, 2010.
- [5] Dilena M., Morassi A., Limongelli M., Vibration based methods for damage localization in bridges, EVACES’13 – Experimental Vibration Analysis for Civil Engineering Structures, Ouro Preto, Brazil, 329–338, 28-30 October 2013.
- [6] Das S., Saha P., Patro S.K., Vibration-based damage detection techniques used for health monitoring of structures: A review, J Civ Struct Heal Monit, 6, 477–507, 2016.
- [7] Zheng D.Y., Fan S.C., Natural frequencıes of a non-uniform beam with multiple cracks via modified Fourier series, J Sound Vib, 242, 701–717, 2001.
- [8] Mazanoglu K., Yesilyurt I., Sabuncu M., Vibration analysis of multiple-cracked non-uniform beams, J Sound Vib, 320, 977–989, 2009.
- [9] Mazanoglu K., Sabuncu M., Vibration analysis of non-uniform beams having multiple edge cracks along the beam’s height, Int J Mech Sci, 52, 515–522, 2010.
- [10] Zhang K., Yan X., Multi-cracks identification method for cantilever beam structure with variable cross-sections based on measured natural frequency changes, J Sound Vib, 387, 53–65, 2017.
- [11] Tan G., Liu Z., Shan J., Wu C., Direct and inverse problems on free vibration analysis of cracked non-uniform beams carrying spring-mass systems by finite element method, Vibroengineering Procedia, 14, 7–12, 2017.
- [12] Tan G., Liu Y., Gong Y., Shen Y., Liu Z., Free vibration of the cracked non-uniform beam with cross section varying as polynomial functions, KSCE J Civ Eng, 22, 4530–4546, 2018.
- [13] Wu J.S., Chen D.W., Bending vibrations of wedge beams with any number of point masses, J Sound Vib, 262, 1073–1090, 2003.
- [14] Hsu J.C., Lai H.Y., Chen C.K., Free vibration of non-uniform Euler-Bernoulli beams by the Adomian modified decomposition method, J Sound Vib, 318, 965–981, 2008.
- [15] Tan G., Wang W., Jiao Y., Flexural free vibrations of multistep nonuniform beams, Math Probl Eng, Article ID 7314280, 1–12, 2016.
- [16] Zhou D., Cheung Y.K., Free vibration of a type of tapered beams, Comput Methods Appl Mech Eng, 188, 203–216, 2000.
- [17] Zhou D., Cheung Y.K., Vibrations of tapered Timoshenko beams in terms of static Timoshenko beam functions, J Appl Mech, 68, 596–602, 2001.
- [18] Bazoune A., Khulief Y.A., Stephen N.G., Shape functions of three-dimensional Timoshenko beam element, J Sound Vib, 259, 473–480, 2003.
- [19] He P., Liu Z., Li C., An improved beam element for beams with variable axial parameters, Shock Vib, 20, 601–617, 2013.
- [20] Tudjono S., Han A., Nguyen D.K., Kiryu S., Gan B.S., Exact shape functions for Timoshenko beam element, IOSR J Comput Eng, 19, 12–20, 2017.
- [21] Dessi D., Camerlengo G., Damage identification techniques via modal curvature analysis: Overview and comparison, Mech Syst Signal Process, (52–53), 181–205, 2015.
- [22] Qiao P., Lu K., Lestari W., Wang J., Curvature mode shape-based damage detection in composite laminated plates, Compos Struct, 80, 409–428, 2007.
- [23] Lestari W., Qiao P., Hanagud S., Curvature mode shape-based damage assessment of carbon/epoxy composite beams, J Intell Mater Syst Struct, 18, 189–208, 2007.
- [24] ANSYS. Mechanical APDL Release 16.0 2014.
Year 2021,
Volume: 36 Issue: 2, 841 - 854, 05.03.2021
Abstract
References
- [1] Salawu O.S., Detection of structural damage through changes in frequency: A review, Eng Struct, 19, 718–723, 1997.
- [2] Doebling S.W., Farrar C.R., Prime M.B., A summary review of vibration-based damage identification methods, Shock Vib Dig, 30, 91–105, 1998.
- [3] Sinou J.J., A Review of Damage Detection and Health Monitoring of Mechanical Systems from Changes in the Measurement of Linear and Non-Linear Vibrations, Mechanical Vibrations: Measurements, Effects and Control, Editor: Sapri R.C., Nova Science Publishers, Inc., 643–702, 2009.
- [4] Farrar C.R., Worden K., An introduction to structural health monitoring, CISM International Centre for Mechanical Sciences, Courses and Lectures, 365(1851), 303–315, 2010.
- [5] Dilena M., Morassi A., Limongelli M., Vibration based methods for damage localization in bridges, EVACES’13 – Experimental Vibration Analysis for Civil Engineering Structures, Ouro Preto, Brazil, 329–338, 28-30 October 2013.
- [6] Das S., Saha P., Patro S.K., Vibration-based damage detection techniques used for health monitoring of structures: A review, J Civ Struct Heal Monit, 6, 477–507, 2016.
- [7] Zheng D.Y., Fan S.C., Natural frequencıes of a non-uniform beam with multiple cracks via modified Fourier series, J Sound Vib, 242, 701–717, 2001.
- [8] Mazanoglu K., Yesilyurt I., Sabuncu M., Vibration analysis of multiple-cracked non-uniform beams, J Sound Vib, 320, 977–989, 2009.
- [9] Mazanoglu K., Sabuncu M., Vibration analysis of non-uniform beams having multiple edge cracks along the beam’s height, Int J Mech Sci, 52, 515–522, 2010.
- [10] Zhang K., Yan X., Multi-cracks identification method for cantilever beam structure with variable cross-sections based on measured natural frequency changes, J Sound Vib, 387, 53–65, 2017.
- [11] Tan G., Liu Z., Shan J., Wu C., Direct and inverse problems on free vibration analysis of cracked non-uniform beams carrying spring-mass systems by finite element method, Vibroengineering Procedia, 14, 7–12, 2017.
- [12] Tan G., Liu Y., Gong Y., Shen Y., Liu Z., Free vibration of the cracked non-uniform beam with cross section varying as polynomial functions, KSCE J Civ Eng, 22, 4530–4546, 2018.
- [13] Wu J.S., Chen D.W., Bending vibrations of wedge beams with any number of point masses, J Sound Vib, 262, 1073–1090, 2003.
- [14] Hsu J.C., Lai H.Y., Chen C.K., Free vibration of non-uniform Euler-Bernoulli beams by the Adomian modified decomposition method, J Sound Vib, 318, 965–981, 2008.
- [15] Tan G., Wang W., Jiao Y., Flexural free vibrations of multistep nonuniform beams, Math Probl Eng, Article ID 7314280, 1–12, 2016.
- [16] Zhou D., Cheung Y.K., Free vibration of a type of tapered beams, Comput Methods Appl Mech Eng, 188, 203–216, 2000.
- [17] Zhou D., Cheung Y.K., Vibrations of tapered Timoshenko beams in terms of static Timoshenko beam functions, J Appl Mech, 68, 596–602, 2001.
- [18] Bazoune A., Khulief Y.A., Stephen N.G., Shape functions of three-dimensional Timoshenko beam element, J Sound Vib, 259, 473–480, 2003.
- [19] He P., Liu Z., Li C., An improved beam element for beams with variable axial parameters, Shock Vib, 20, 601–617, 2013.
- [20] Tudjono S., Han A., Nguyen D.K., Kiryu S., Gan B.S., Exact shape functions for Timoshenko beam element, IOSR J Comput Eng, 19, 12–20, 2017.
- [21] Dessi D., Camerlengo G., Damage identification techniques via modal curvature analysis: Overview and comparison, Mech Syst Signal Process, (52–53), 181–205, 2015.
- [22] Qiao P., Lu K., Lestari W., Wang J., Curvature mode shape-based damage detection in composite laminated plates, Compos Struct, 80, 409–428, 2007.
- [23] Lestari W., Qiao P., Hanagud S., Curvature mode shape-based damage assessment of carbon/epoxy composite beams, J Intell Mater Syst Struct, 18, 189–208, 2007.
- [24] ANSYS. Mechanical APDL Release 16.0 2014.
There are 24 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | March 5, 2021 |
| Submission Date | March 29, 2020 |
| Acceptance Date | October 20, 2020 |
| Published in Issue | Year 2021 Volume: 36 Issue: 2 |