Dynamic Stability Analysis of a Composite Curved Beam with Suspended Mass-Spring Systems

Year 2020, Volume: 25 Issue: 3, 1557 - 1576, 31.12.2020

Seda Vatan Can , Hasan Öztürk

https://doi.org/10.17482/uumfd.793121

Cited By: 1

Abstract

In this study, the dynamic stability of a laminated composite curved beam with a suspended mass-spring system is investigated. The composite curved beam is considered as a uniform cross-sectional area Euler-Bernoulli beam and effective flexibility module is utilized. The curved beam model is obtained by using the Bolotin approach and the finite element model based on energy equations. The natural frequencies of the composite curved beam obtained with a finite element code developed in MATLAB are compared with the results of ANSYS model. It is found that the results are very good agreement. The effects of the number and position of the suspended mass-spring system on the instability regions of the beam are surveyed considered that also dynamic load parameter and static load parameter for different fiber orientation angles of the layered composite curved beam. The dynamic stability regions of both types of the curved beam with and without suspended spring-mass system are presented in figures.

Keywords

curved beam, suspended spring-mass, vibration analysis, dynamic stability, finite elements

ASILI KÜTLE-YAY SİSTEMLERİNE SAHİP KOMPOZİT EĞRİ KİRİŞİN DİNAMİK KARARLILIK ANALİZİ

Abstract

Bu çalışmada, asılı kütle-yay sistemine sahip tabakalı kompozit eğri bir kirişin dinamik kararlılığı araştırılmıştır. Kompozit eğri kiriş sabit kesit alana sahip Euler-Bernoulli kirişi olarak dikkate alınmış ve etkin esneklik modülü kullanılmıştır. Bolotin yaklaşımı ve enerji denklemlerine dayanan sonlu elemanlar yöntemi kullanılarak eğri kiriş modeli oluşturulmuştur. MATLAB’de geliştirilen bir sonlu elemanlar kodu ile elde edilen kompozit eğri kirişe ait doğal frekanslar, ANSYS programında elde edilen sonuçlar ile karşılaştırılmıştır. Sonuçların tutarlı olduğu görülmüştür. Tabakalı kompozit eğri kirişin farklı fiber açıları için asılı kütle-yay sisteminin sayısının ve konumunun kirişin kararsızlık bölgelerine etkileri, dinamik yük parametresi ve statik yük parametresi de dikkate alınarak incelenmiştir. Asılı kütle-yay sistemi olmayan eğri kiriş ve asılı kütle-yay sistemine sahip eğri kirişe ait dinamik kararsızlık bölgeleri şekillerle sunulmuştur.

Keywords

eğri kiriş, asılı kütle-yay, titreşim analizi, dinamik kararlılık, sonlu elemanlar

References

• Ahmed, K. M. (1971) Free vibration of curved sandwich beams by the method of finite elements. Journal of Sound and Vibration, 18(1), 61-74. doi:10.1016/0022-460X(71)90631- 6
• Bolotin, V. V. (1962) The dynamic stability of elastic systems. San Francisco, CA: Holden- Day, Inc.
• Briseghella, L., Majorana, C.E. ve Pellegrino, C. (1998) Dynamic stability of elastic structures: a finite element approach. Computers & Structures, 69(1), 11-25. doi:10.1016/S0045-7949(98)00084-4
• Chang, C.S. ve Hodges, D.H. (2009) Vibration characteristics of curved beams. Journal of Mechanics of Materials and Structures, 4(4), 675-692. doi:10.2140/jomms.2009.4.675
• Chen, LW. ve Shen, G.S. (1998) Vibration and buckling of initially stressed curved beams. Journal of Sound and Vibration, 215(3), 511-526. doi: 10.1006/jsvi.1998.1680
• Chen, L.W., Lin, C.Y. ve Wang, C.C. (2002) Dynamic stability analysis and control of a composite beam with piezoelectric layers. Composite Structures, 56(1), 97-109. doi: 10.1016/S0263-8223(01)00183-0
• Çankaya, P., Sabuncu, M. ve Öztürk, H. (2017) Asılı Kütle-Yay Sistemlerine Sahip Eğri Çubuğun Titreşim Analizi. Sempozyum: 18. Ulusal Makine Teorisi Sempozyumu, (387-391).
• Daş, M. T. ve Yılmaz, A. (2018a). Çatlaklı dairesel eğri kompozit kirişlerin titreşim analizleri. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 33(3), 783-792. doi: 10.17341/gazimmfd.416380
• Das, M. T., & Yılmaz, A. (2018b). Experimental modal analysis of curved composite beam with transverse open crack. Journal of Sound and Vibration, 436, 155-164. doi: 10.1016/j.jsv.2018.09.021
• Eisenberger M. ve Efraim E. (2001) In-plane vibration of shear deformable curved beams. International Journal for Numerical Methods in Engineering, 52(11):1221–34. doi:10.1002/nme.246
• Eroğlu, U., Ruta, G. ve Tüfekçi, E. (2019). Natural frequencies of parabolic arches with a single crack on opposite cross-section sides. Journal of Vibration and Control, 25(7), 1313- 1325. doi: 10.1177/1077546319825681
• Eroğlu, U. ve Tüfekçi E. (2018) A new finite element formulation for free vibrations of planar curved beams. Mechanics Based Design of Structures and Machines, 46(6):730–50. doi:10.1080/15397734.2018.1456343
• Günyar, A., Öztürk, H. ve Sabuncu, M. (2012a) Kompozit eğri çubukların doğal frekans ve burkulma yükü analizi. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 14(3), 33-42. doi:20.500.12397/2461
• Günyar, A., Öztürk, H. ve Sabuncu, M., (2012b) Dynamic stability analysis of laminated curved beams. DEU Mühendislik Fakültesi Mühendislik Bilimleri Dergisi, 14(42), 43-55. doi: 20.500.12397/2458
• Huang, C.S., Tseng Y.P., Leissa A.W. ve Nieh K.Y. (1998) An exact solution for in-plane vibrations of an arch having variable curvature and cross-section. International Journal of Mechanical Sciences, 40(11):1159–73. doi:10.1016/S0020-7403(98)00020-4
• Huang, C.S., Nieh K.Y. ve Yang M.C. (2003) In-plane free vibration and stability of loaded and shear-deformable circular arches. International Journal of Solids and Structures, 40(22):5865–86. doi: 10.1016/S0020-7683(03)00393-7
• Jun, L., Guangwei R., Jin P., Xiaobin L. ve Weiguo W. (2014) Free vibration analysis of a laminated shallow curved beam based on trigonometric shear deformation theory. Mechanics Based Design of Structures and Machines, 42(1):111–29. doi: 10.1080/15397734.2013.846224
• Karaağaç, C., Öztürk, H. ve Sabuncu, M. (2007) Lateral dynamic stability analysis of a cantilever laminated composite beam with an elastic support. International Journal of Structural Stability and Dynamics, 7(03), 377-402. doi: 10.1142/S0219455407002320
• Karami, G., ve Malekzadeh P. (2004) In-plane free vibration analysis of circular arches with varying cross-sections using differential quadrature method. Journal of Sound and Vibration, 274(3–5):777–99. doi: 10.1016/S0022-460X(03)00786-7
• Karami, B., Janghorban M., Shahsavari D., Dimitri R. ve Tornabene F. (2019) Nonlocal buckling analysis of composite curved beams reinforced with functionally graded carbon nanotubes. Molecules, 24(15):2750. doi: 10.3390/molecules24152750
• Kaw, A.K. (2005) Mechanics of Composite Materials. CRC Press.
• Kawakami, M., Sakiyama T., Matsuda H., and Morita C. (1995) In-plane and out-of-plane free vibrations of curved beams with variable cross-sections. Journal of Sound and Vibration, 187 (3):381–401. doi: 10.1006/jsvi.1995.0531
• Kıral, B.G., Kıral, Z. ve Öztürk, H. (2015) Stability analysis of delaminated composite beams. Composites Part B Engineering, 79, 406-418. doi: 10.1016/j.compositesb.2015.05.008
• Kiss, L. ve Szeidl G. (2015) Vibrations of pinned–pinned heterogeneous circular beams subjected to a radial force at the crown point. Mechanics Based Design of Structures and Machines, 43(4):424–49. doi:10.1080/15397734.2015.1022659
• Kovács, B. (2013) Vibration analysis of layered curved arch. Journal of Sound and Vibration, 332(18), 4223-4240. doi:10.1016/j.jsv.2013.03.011
• Lee, B.K., ve Wilson J.F. (1990) Free vibrations of arches with variable curvature. Journal of Sound and Vibration, 136(1):75–89. doi:10.1016/0022-460X(90)90939-W
• Lim, N.H. ve Kang, Y.J. (2004) Out of plane stability of circular arches. International Journal of Mechanical Sciences, 46(8), 1115-1137. doi:10.1016/j.ijmecsci.2004.08.008
• Matsunaga, H. (2004) Free vibration and stability of laminated composite circular arches subjected to initial axial stress. Journal of Sound and Vibration, 271(3-5), 651-670. doi:10.1016/S0022-460X(03)00298-0
• Öztürk, H. ve Sabuncu, M. (2005) Stability analysis of a cantilever composite beam on elastic supports. Composites Science and Technology, 65(13), 1982-1995. doi:10.1016/j.compscitech.2005.03.004
• Öztürk, H., Yeşilyurt, İ. ve Sabuncu, M. (2006) In-plane stability analysis of non-uniform cross-sectioned curved beams. Journal of Sound and Vibration, 296(1-2), 277-291. doi:10.1016/j.jsv.2006.03.002
• Petyt, M. ve Fleischer, C.C. (1971) Free vibration of a curved beam. Journal of Sound and Vibration, 18 (1), 17-30. doi:10.1016/0022-460X(71)90627-4
• Rao, S. S. ve Sundararajan, V. (1969) In-plane flexural vibrations of circular rings. Journal of Applied Mechanics, 36(3), 620-625. doi: 10.1115/1.3564726
• Rattanawangcharoen, N., Bai, H. ve Shah, A.H. (2004) A 3D cylindrical finite element model for thick curved beam stress analysis. International journal for numerical methods in engineering, 59(4), 511-531. doi:10.1002/nme.888
• Sabir, A.B. ve Ashwell, D.G. (1971) A comparison of curved beam finite elements when used in vibration problems. Journal of Sound and Vibration, 18 (4), 555-563. doi: 10.1016/0022- 460X(71)90106-4
• Sabuncu, M. (1978) Vibration characteristics of rotating aerofoil cross-section bladed-disc assembly. PhD Thesis, Surrey University, Surrey.
• Sahu, S. K. ve Datta, P.K. (2003) Dynamic stability of laminated composite curved panels with cutouts. Journal of Engineering Mechanics, 129(11), 1245-1253. doi:10.1061/(ASCE)0733-9399(2003)129:11(1245)
• Thomas, J. ve Abbas, B.A.H. (1975) Finite element model for dynamic analysis of Timoshenko beam. Journal of Sound and Vibration, 41(3), 291-299. doi: 10.1016/S0022- 460X(75)80176-3
• Tong, X., Mrad, N. ve Tabarrok, B. (1998) In-plane vibration of circular arches with variable cross-sections. Journal of Sound and Vibration, 212(1), 121-140. doi:10.1006/jsvi.1997.1441
• Tüfekçi, E. ve Yiğit, O. O. (2013). In-plane vibration of circular arches with varying cross- sections. International Journal of Structural Stability and Dynamics, 13(01), 1350003. doi:10.1142/S021945541350003X
• Vatan Can, S., Çankaya, P., Öztürk, H. ve Sabuncu, M. (2020) Vibration and dynamic stability analysis of curved beam with suspended spring–mass systems. Mechanics Based Design of Structures and Machines, 1-15. (basımda) doi:10.1080/15397734.2020.1737111
• Wu, J.S., Lin, F.T. ve Shaw, H.J. (2013) Free in-plane vibration analysis of a curved beam (arch) with arbitrary various concentrated elements. Applied Mathematical Modelling, 37(14- 15), 7588-7610. doi:10.1016/j.apm.2013.02.029
• Yang, F., Sedaghati, R. ve Esmailzadeh, E. (2008) Free in-plane vibration of general curved beams using finite element method. Journal of Sound and Vibration, 318(4-5), 850-867. doi:10.1016/j.jsv.2008.04.041
• Zare, M. (2020) Free out-of-plane vibration of cracked curved beams on elastic foundation by estimating the stress intensity factor. Mechanics of Advanced Materials and Structures, 27(14), 1238-1245. doi:10.1080/15376494.2018.1506068