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Ucunda ekleme bulunan elastik mesnetli konsol Timoshenko kirişin serbest titreşim analizi

Yıl 2023, Cilt: 29 Sayı: 3, 274 - 280, 27.06.2023

Öz

Bu çalışmada ucunda eklemeler olan bir konsol Timoshenko kirişin titreşim analizi yapılmıştır. Kirişin, serbest ucunda lineer yay ile bağlanmış kütle taşıdığı ve sol ucunda dönme yayı bulunduğu varsayılmıştır. Bu kabullere göre doğal frekanslar ve mod şekilleri, kütlenin, serbest uca bağlı lineer yayın ve dönme yayının etkilerini tanımlayan boyutsuz parametreler cinsinden elde edilmiştir. Sonuçlar tablolaştırılmış ve bazı parametreler için Timoshenko ve EulerBernoulli kiriş yaklaşımlarının karşılaştırılması yapılmıştır. Sonuçlar göstermiştir ki doğal frekanslar uç kütlesinin artması ile düşmektedir. Burulma yayı sabitinin büyük değerleri, yüksek doğal frekansları ortaya çıkartmaktadır.

Kaynakça

  • [1] Low KH. “On the methods to derive frequency equations of beams carrying multiple masses”. International Journal of Mechanical Sciences, 43(3), 871-881, 2001.
  • [2] Majkut L. “Free and forced vibrations of Timoshenko beams described by single difference equation”. Journal of Theoretical and Applied Mechanics, 47(1), 193-210, 2009.
  • [3] Laura PAA, Pombo JL, Susemihl EA. “A note on the vibrations of a clamped-free beam with a mass at the free end”. Journal of Sound and Vibration, 37(2), 161-168, 1974.
  • [4] Chang CH. “Free vibration of a simply supported beam carrying a rigid mass at the middle”. Journal of Sound and Vibration, 237(4), 733-744, 2000.
  • [5] Banerjee JR. “Free vibration of beams carrying springmass systems-a dynamic stiffness approach”. Computers and Structures, 104-105, 21-26, 2012.
  • [6] Rossit CA, Laura PAA. “Free vibrations of a cantilever beam with a spring-mass system attached to the free end”. Ocean Engineering, 28(7), 933-939, 2001.
  • [7] Stephen NG. “The second frequency spectrum of Timoshenko beams”. Journal of Sound and Vibration, 80(4), 578-582, 1982.
  • [8] Dym CL, Shames IH. Solid Mechanics, A Variational Approach. Augmented ed. New York, USA, Springer, 2013.
  • [9] Zhu X, Li TY, Zhao Y, Liu JX.“Structural power flow analysis of Timoshenko beam with an open crack”. Journal of Sound and Vibration, 297(1-2), 215-226, 2006.
  • [10] Yuan S, Ye K, Xiao C, Williams FW, Kennedy D. “Exact dynamic stiffness method for non-uniform Timoshenko beam vibrations and Bernoulli-Euler column buckling”. Journal of Sound and Vibration, 303(3-5), 526-537, 2007.
  • [11] Rossit CA, Laura PAA. “Transverse, normal modes of vibration of a cantilever Timoshenko beam with a mass elastically mounted at the free end”. The Journal of the Acoustical Society of America, 110(6), 2837-2840, 2001.
  • [12] Abramovich H, Hamburger O. “Vibration of a uniform cantilever Timoshenko beam with translational and rotational springs and with a tip mass”. Journal of Sound and Vibration, 154(1), 67-80, 1992.
  • [13] Salarieh H, Ghorashi M. “Free vibration of Timoshenko beam with finite mass rigid tip load and flexural-torsional coupling”. International Journal of Mechanical Sciences, 48(7), 763-779, 2006.
  • [14] Jafari-Talookolaei RA, Abedi M. “An exact solution for the free vibration analysis of Timoshenko beams”. Review of Applied Physics, 3, 12-17, 2014.
  • [15] Kati HD, Gokdag H. “Vibration analysis of a Timoshenko beam carrying 3D tip mass by using differential transform method”. Structural Engineering and Mechanics, 65(4), 381-388, 2018.
  • [16] Torabi K, Afshari H, Heidari-Rarani M. "Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM". Engineering Solid Mechanics, 1(1), 9-20, 2013.
  • [17] Cekus D. “Free Vibration of a Cantilever Tapered Timoshenko Beam”. Scientific Research of the Institute of Mathematics and Computer Science, 11(4), 11-17, 2012.
  • [18] Yuan J, Pao YH, Chen W. “Exact solutions for free vibrations of axially inhomogeneous Timoshenko beams with variable cross section”. Acta Mechanica, 227, 2625-2643, 2016.
  • [19] Rao SS. Mechanical Vibrations. 5th ed. NJ, USA, Pearson Education Inc., 2011.

Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments

Yıl 2023, Cilt: 29 Sayı: 3, 274 - 280, 27.06.2023

Öz

This paper investigates the lateral vibration of a cantilever Timoshenko beam with attachments. It is assumed that the beam carries a mass attached to the free end with a linear spring and there exists a rotational spring at the left end. Depending upon these assumptions, mode shapes and natural frequencies are obtained in terms of nondimensional parameters which describe the effects of additional mass, linear spring and rotational spring. The results are tabulated, and the comparison of Timoshenko and Euler-Bernoulli beam approaches are carried out for some parameters. Results reveal that natural frequencies decrease while the values of end mass increase. Large values of the rotational spring constant cause high natural frequencies.

Kaynakça

  • [1] Low KH. “On the methods to derive frequency equations of beams carrying multiple masses”. International Journal of Mechanical Sciences, 43(3), 871-881, 2001.
  • [2] Majkut L. “Free and forced vibrations of Timoshenko beams described by single difference equation”. Journal of Theoretical and Applied Mechanics, 47(1), 193-210, 2009.
  • [3] Laura PAA, Pombo JL, Susemihl EA. “A note on the vibrations of a clamped-free beam with a mass at the free end”. Journal of Sound and Vibration, 37(2), 161-168, 1974.
  • [4] Chang CH. “Free vibration of a simply supported beam carrying a rigid mass at the middle”. Journal of Sound and Vibration, 237(4), 733-744, 2000.
  • [5] Banerjee JR. “Free vibration of beams carrying springmass systems-a dynamic stiffness approach”. Computers and Structures, 104-105, 21-26, 2012.
  • [6] Rossit CA, Laura PAA. “Free vibrations of a cantilever beam with a spring-mass system attached to the free end”. Ocean Engineering, 28(7), 933-939, 2001.
  • [7] Stephen NG. “The second frequency spectrum of Timoshenko beams”. Journal of Sound and Vibration, 80(4), 578-582, 1982.
  • [8] Dym CL, Shames IH. Solid Mechanics, A Variational Approach. Augmented ed. New York, USA, Springer, 2013.
  • [9] Zhu X, Li TY, Zhao Y, Liu JX.“Structural power flow analysis of Timoshenko beam with an open crack”. Journal of Sound and Vibration, 297(1-2), 215-226, 2006.
  • [10] Yuan S, Ye K, Xiao C, Williams FW, Kennedy D. “Exact dynamic stiffness method for non-uniform Timoshenko beam vibrations and Bernoulli-Euler column buckling”. Journal of Sound and Vibration, 303(3-5), 526-537, 2007.
  • [11] Rossit CA, Laura PAA. “Transverse, normal modes of vibration of a cantilever Timoshenko beam with a mass elastically mounted at the free end”. The Journal of the Acoustical Society of America, 110(6), 2837-2840, 2001.
  • [12] Abramovich H, Hamburger O. “Vibration of a uniform cantilever Timoshenko beam with translational and rotational springs and with a tip mass”. Journal of Sound and Vibration, 154(1), 67-80, 1992.
  • [13] Salarieh H, Ghorashi M. “Free vibration of Timoshenko beam with finite mass rigid tip load and flexural-torsional coupling”. International Journal of Mechanical Sciences, 48(7), 763-779, 2006.
  • [14] Jafari-Talookolaei RA, Abedi M. “An exact solution for the free vibration analysis of Timoshenko beams”. Review of Applied Physics, 3, 12-17, 2014.
  • [15] Kati HD, Gokdag H. “Vibration analysis of a Timoshenko beam carrying 3D tip mass by using differential transform method”. Structural Engineering and Mechanics, 65(4), 381-388, 2018.
  • [16] Torabi K, Afshari H, Heidari-Rarani M. "Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM". Engineering Solid Mechanics, 1(1), 9-20, 2013.
  • [17] Cekus D. “Free Vibration of a Cantilever Tapered Timoshenko Beam”. Scientific Research of the Institute of Mathematics and Computer Science, 11(4), 11-17, 2012.
  • [18] Yuan J, Pao YH, Chen W. “Exact solutions for free vibrations of axially inhomogeneous Timoshenko beams with variable cross section”. Acta Mechanica, 227, 2625-2643, 2016.
  • [19] Rao SS. Mechanical Vibrations. 5th ed. NJ, USA, Pearson Education Inc., 2011.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Makine Mühendisliği (Diğer)
Bölüm Makale
Yazarlar

Yasar Pala Bu kişi benim

Caglar Kahya Bu kişi benim

Yayımlanma Tarihi 27 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 29 Sayı: 3

Kaynak Göster

APA Pala, Y., & Kahya, C. (2023). Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 29(3), 274-280.
AMA Pala Y, Kahya C. Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. Haziran 2023;29(3):274-280.
Chicago Pala, Yasar, ve Caglar Kahya. “Free Vibration Analysis of Elastically Restrained Cantilever Timoshenko Beam With Attachments”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 29, sy. 3 (Haziran 2023): 274-80.
EndNote Pala Y, Kahya C (01 Haziran 2023) Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 29 3 274–280.
IEEE Y. Pala ve C. Kahya, “Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, c. 29, sy. 3, ss. 274–280, 2023.
ISNAD Pala, Yasar - Kahya, Caglar. “Free Vibration Analysis of Elastically Restrained Cantilever Timoshenko Beam With Attachments”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 29/3 (Haziran 2023), 274-280.
JAMA Pala Y, Kahya C. Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2023;29:274–280.
MLA Pala, Yasar ve Caglar Kahya. “Free Vibration Analysis of Elastically Restrained Cantilever Timoshenko Beam With Attachments”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, c. 29, sy. 3, 2023, ss. 274-80.
Vancouver Pala Y, Kahya C. Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2023;29(3):274-80.





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