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Değişken Kesitli Kirişlerin Genel Sınır Şartları İçin Titreşim Analizi

Yıl 2021, Cilt: 22 Sayı: 2, 73 - 86, 31.12.2021

Öz

Bu çalışmada değişken kesitli izotropik kirişin serbest titreşimi incelenmiştir. Seçilen kiriş genişliği üstel olarak değişken olduğundan yönetici denklemler uzay koordinatlarında benzer kesit geometrileri için adi diferansiyel denklemler haline indirgenmiştir. Kiriş titreşimine ait analitik çözümler ankastre, basit mesnetli ve serbest uçlu olmak üzere bütün sınır koşulları için ayrı ayrı hesaplanmıştır. Mod şekilleri ve doğal frekanslar her bir sınır şartı için bulunmuştur. Sonuçlar kiriş kesitindeki değişimin mod şekillerini ve doğal frekansları etkilediğini göstermektedir. Titreşimin frekansı genişleyen kesitlerde artmakta daralan kesitlerde ise azalmaktadır.

Kaynakça

  • [1] İ.Varserin, “Kesidi Üstel Olarak Değişen Kirişlerin Serbest Titreşim Analizi,” Yüksek Lisans Tezi, Makine Mühendisliği Bölümü, Trakya Üniversitesi, Edirne, Türkiye, 2015.
  • [2] D.J. Gorman, Free vibration analysis of beams and shafts, 1. Baskı, New York, USA, Wiley, 1975.
  • [3] E.T. Cranch, A.A. Adler, “Bending vibration of variable section beams,” Journal of Applied Mechanics, c. 23, s. 1, ss. 103–108, 1956.
  • [4] H.D. Conway, J.F. Dubil, “Vibration frequencies of truncated-cone and wedge beams,” Journal of Applied Mechanics, c. 32, s.4, ss. 932–934, 1965.
  • [5] A.C. Heidebrecht, “Vibration of non-uniform simply supported beams,” Journal of the Engineering Mechanics Division, c.93, s. 2, ss. 1–15, 1967.
  • [6] R.M. Branch, “On the extremal fundamental frequencies of vibrating beams,” Journal of Sound and Vibration, c. 4, ss. 667–674, 1968.
  • [7] H.H. Mabie, C.B. Rogers, “Transverse vibration of double-tapered cantilever beams,” Journal of the Acoustical Society of America, c. 51, s. 5, ss. 1771–1775, 1972.
  • [8] C.D. Bailey, “Direct analytical solution to non-uniform beam problems,” Journal of Sound and Vibration, c. 56, s. 4, ss. 501–507, 1978.
  • [9] N. Olhoff, R. Parbery, "Designing vibrating beams and rotating shafts for maximum difference between adjacent natural frequencies," International Journal of Solids and Structures, c. 20, ss. 63-75, 1984.
  • [10] A.K. Gupta, “Vibration of tapered beams,” Journal of Structural Engineering, c. 111, s. 1, ss. 19–36, 1985.
  • [11] R. Jategaonkar, D.S. Chehil, “Natural frequencies of a beam with varying section properties,” Journal of Sound and Vibration, c. 133, ss. 303–322, 1989.
  • [12] S. Naguleswaran, “Vibration of an Euler–Bernoulli beam of constant depth and with linearly varying breadth,” Journal of Sound and Vibration, c. 153 s. 3, ss. 509–522, 1992.
  • [13] S. Naguleswaran, “A direct solution for the transverse vibration of Euler–Bernoulli wedge and cone beams,” Journal of Sound and Vibration, c. 172, s. 3, ss. 289–304, 1994a.
  • [14] Naguleswaran S. “Vibration in Two Princible Planes of a Non-uniform Beam of Rectangular Cross-Section, One Side of Which Varies as a Square Root of the Axial Coordinate,” Journal of Sound and Vibration, c. 172, s. 3, ss. 305-319, 1994b.
  • [15] P.A.A. Laura, R.H. Gutierrez, R.E. Rossi, “Free vibration of beams of bi-linearly varying thickness,” Ocean Engineering, c. 23, s. 1, ss. 1–6, 1996.
  • [16] A.K. Datta, S.N. Sil, “An analysis of free undamped vibration of beams of varying cross-section,” Computers and Structures, c. 59, s. 3, ss. 479–483, 1996.
  • [17] D.Caruntu, “On nonlinear vibration of non-uniform beam with rectangular cross-section and parabolic thickness variation,” IUTAM / IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems, Solid Mechanics and Its Applications, London, ss. 109–118, 2000.
  • [18] I. Elishakoff, V. Johnson, “Apparently the first closed-form solution of vibrating inhomogeneous beam with a tip mass,” Journal of Sound and Vibration, c. 286, s. 4-5, ss. 1057–1066, 2005.
  • [19] S.K. Jang, C.W. Bert, “Free vibration of stepped beams,” Exact and numerical solutions. Journal of Sound and Vibration, c. 130, ss. 342–346, 1989a.
  • [20] S.K. Jang, C.W. Bert, “Free vibration of stepped beams: Higher mode frequencies and effects of steps on frequencies,” Journal of Sound and Vibration, c. 32, ss. 164–168, 1989b.
  • [21] I. Elishakoff, Eigenvalues of inhomogeneous structures: unusual closed-form solutions, CRC Press, Boca Raton, 2005.
  • [22] M.C. Ece, M. Aydoğdu, V. Taşkın, “Vibration of variable cross-section beam,” Mechanics Research Communications, c. 34, ss. 78-84, 2007.
  • [23] M. Aydogdu, S. Filiz, “Vibration Analysis of Piecewise and Continuously Axially Graded Rods and Beams,” Mechanical Vibrations: Types, Testing and Analysis, ss. 95-145, Nova Science Publishers, Inc. 2010.
  • [24] B. Akgöz, Ö. Civalek, “Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory,” Composite Structures, c. 98, ss. 314–322, 2013.
  • [25] A. Mirzabeigy, “Semi-analytical Approach for Free Vibration Analysis of Variable Cross-section Beams Resting on Elastic Foundation and under Axial Force,” IJE Transactions C: Aspects, c. 27, ss. 385-394, 2014.
  • [26] F.F. Calim, “Transient analysis of axially functionally graded Timoshenko beams with variable cross-section,” Composites Part B, c. 98, ss. 472-483, 2016.
  • [27] B.H. Khaniki, S.H. Hashemi, “ Free Vibration Analysis of Nonuniform Microbeams Based on Modified Couple Stress Theory: an Analytical Solution,” IJE TRANSACTIONS B: Applications, c. 30 ss. 311-320, 2017.
  • [28] F.F. Çalım, “Değişken Kesitli Timoshenko Kirişinin Serbest Titreşim Analizi,” Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, c. 6, s. 1, ss. 76-82, 2017.
  • [29] F. Sohani, H.R. Eipakchi, “Analytical solution for modal analysis of Euler- Bernoulli and Timoshenko beam with an arbitrary varying cross-section,” Mathematical Models in Engineering, c. 4, s. 3, 2018.
  • [30] S. Sınır, M. Çevik, B.G. Sınır, “Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section,” Composites Part B, c. 148, ss. 123–131, 2018.
  • [31] E. Demir, “Longitudinal vibration of temperature dependent bar with variable cross-section,” Politeknik Dergisi, c. 21, s. 4, ss. 813-819, 2018.
  • [32] H. Lohar, A. Mitra, S. Sahoo, “Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation,” International Frontier Science Letters, c. 9, ss. 9-25, 2016.
  • [33] M. Soltani, B. Asgarian, “New hybrid approach for free vibration and stability analyses of axially functionally graded Euler-Bernoulli beams with variable cross-section resting on uniform Winkler-Pasternak foundation,” Latin American Journal of Solids and Structures, c. 16, s. 173, 2019.
  • [34] A. Ghannadiasl, “Natural frequencies of the elastically end restrained non-uniform Timoshenko beam using the power series method,” Mechanics Based Design of Structures and Machines, c. 47, ss. 201-214, 2019.
  • [35] P.A. Demirhan, “Fonksiyonel Derecelendirilmiş Sandviç Kiriş Ve Plakların Dört Değişkenli Kayma Deformasyon Teorisi İle Eğilme Ve Titreşim Analizi”, Doktora Tezi, Makine Mühendisliği Bölümü, Trakya Üniversitesi, Edirne, Türkiye, 2016.
  • [36] X. Tong, B. Tabarrok, “Vibration analysis of Timeshenko beams with non-homogeneity and varying cross-section”. Journal of Sound and Vibration, c. 186 s. 5, ss. 821-835. 1995.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Araştırma Makaleleri
Yazarlar

Vedat Taşkın 0000-0002-3013-2317

İsmail Varserin Bu kişi benim 0000-0002-0766-7452

Pınar Aydan Demirhan 0000-0002-2618-4982

Erken Görünüm Tarihi 9 Ocak 2022
Yayımlanma Tarihi 31 Aralık 2021
Kabul Tarihi 21 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 22 Sayı: 2

Kaynak Göster

IEEE V. Taşkın, İ. Varserin, ve P. A. Demirhan, “Değişken Kesitli Kirişlerin Genel Sınır Şartları İçin Titreşim Analizi”, TUJES, c. 22, sy. 2, ss. 73–86, 2021.