BibTex RIS Kaynak Göster

KALIN CİDARLI İÇİ BOŞ SİLİNDİRLERİN DOĞAL FREKANSLARININ DIŞ/İÇ ÇAP ORANI VE SINIR ŞARTLARI İLE DEĞİŞİMİ

Yıl 2019, Sayı: 15, 3 - 12, 01.08.2019

Vebil Yıldırım

Öz

Bu çalışmada, sonsuz uzunlukta, kalın cidarlı, homojen ve izotrop lineer elastik malzemeden yapılmış içi boş silindirlerin serbest titreşim analizi analitik olarak çalışılmıştır. Öncelikle elastisitenin alan denklemleri kullanılarak, Lame sabitleri cinsinden hareket denklemi elde edilmiş, daha sonra bu denklem Bessel fonksiyonları yardımıyla kapalı olarak çözülmüştür. Her bir olası klasik sınır şartı için, karakteristik serbest titreşim denklemi kapalı formda sunulmuştur. Şimdiki çalışmadan elde edilen sonuçların mevcut literatürle doğrulanması sonrası parametrik bir çalışma gerçekleştirilmiştir. Boyutsuz serbest titreşim frekanslarının sınır şartları ve silindir dış çap/iç çap oranı ile değişimleri grafik olarak gösterilmiş, sonuçların bazıları da tablo halinde sunulmuştur

Anahtar Kelimeler

Serbest Titreşim Doğal Frekans Silindirik Bessel Fonksiyonu Analitik Çözüm

Kaynakça

  • Chree C. The Equations of an Isotropic Elastic Solid in Polar and Cylindrical Coordinates. Their Solutions and Applications. Transactions of the Cambridge Philosophical Society, 1889; 14: 250–309.
  • Greenspon J.E. Flexural Vibrations of a Thick-Walled Circular Cylinder According to the Exact Theory of Elasticity. Journal of Aero/Space Sciences, 1957; 27: 1365–1373.
  • Gladwell G.M., Tahbildar U.C. Finite Element Analysis of Axisymmetric Vibrations of Cylinders. Journal of Sound and Vibration, 1972; 22: 143–157.
  • Hutchinson J.R. Vibrations of Solid Cylinders. Journal of Applied Mechanics, 1980; 47: 901–907.
  • Hutchinson J.R., El-Azhari S.A. Vibrations of Free Hollow Circular Cylinders. Journal of Applied mechanics, 1986; 53: 641–646.
  • Singal R.K., Williams K.A. Theoretical and Experimental Study of Vibrations of Thick Circular Cylindrical Shell and Rings. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1988; 110: 533–537.
  • Ghosh A.K. Axisymmetric Vibration of a Long Cylinder. Journal of Sound and Vibration, 1995; 186(5): 711–721.
  • Gazis D.C. Three Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinder. Journal of the Acoustical Society of America, 1959; 31: 568–578.
  • Leissa A.W., So J. Accurate Vibration Frequencies of Circular Cylinders from Three- Dimensional analysis. Journal of the Acoustical Society of America, 1995; 98: 2136–2141.
  • So J., B Leissa A.W. Free Vibration of Thick Hollow Circular Cylinders from Three- Dimensional analysis. Journal of Vibration and Acoustics, 1997; 119: 89–95.
  • Liew K.M., Hung K.C., Lim M.K. Vibration of Stress Free Hollow Cylinders of Arbitrary Cross-Section. Journal of Applied Mechanics, ASME, 1995; 62: 718–724.
  • Hung K.C., Liew K.M., Lim M.K. Free Vibration of Cantilevered Cylinders: Effects of Cross-Sections and Cavities. Acta Mechanica, 1995; 113: 37–52.
  • Zhou D., Cheung Y.K., Lo S.H., Au F.T.K. 3D Vibration Analysis of Solid and Hollow Circular Cylinders via Chebyshev–Ritz Method. Computer Methods in Applied Mechanics and Engineering, 2003; 192: 1575–1589.
  • Gladwell G.M., Vijay D.K. Natural Frequencies of Free Şnite Length Circular Cylinders. Journal of Sound and Vibration, 1975; 42: 387–397.
  • Wang H., Williams K. Vibrational Modes of Thick Cylinders of Şnite Length. Journal of Sound and Vibration, 1996; 191: 1996, 955–971.
  • Mofakhami M.R., Toudeshky H.H., Hashemi Sh. H. Finite Cylinder Vibrations with Different End Boundary Conditions. Journal of Sound and Vibration, 2006; 297: 293–314.
  • Yıldırım V. Heat-Induced, Pressure-Induced and Centrifugal-Force-Induced Exact Axisymmetric Thermo-Mechanical Analyses in a Thick-Walled Spherical Vessel, an Infinite Cylindrical Vessel, and a Uniform Disk Made of an Isotropic and Homogeneous Material.
  • International Journal of Engineering & Applied Sciences (IJEAS), 2017; 9(2): 66-87. http://dx.doi.org/10.24107/ijeas.309786
  • Watson G.N., “A Treatise on the Theory of Bessel Functions”, Cambridge University Press, 1922.
  • Bowman. F., “Introduction to Bessel Functions”, New York: Dover, 1958.
  • Hildebrand F.B., “Advanced Calculus for Applications”, Prentice-Hall. Inc. Englewood Cliffs, New Jersey, 1962.
  • Abramowitz M., Stegun I.A. (Eds.)., “Handbook of Mathematical Functions with Formulas, Graphs and mathematical tables”, 9th printing, New York, Dover, 1972.
  • Keleş İ., Tütüncü N. Exact Analysis of Axisymmetric Dynamic Response of Functionally Graded Cylinders (or Disks) and Spheres”, Journal of Applied Mechanics, 2011; 78(6): 061014 (7 pages).

Yıl 2019, Sayı: 15, 3 - 12, 01.08.2019

Vebil Yıldırım

Öz

In this study exact free vibration analysis is performed for thick-walled infinite hollow cylinders made of an isotropic and homogeneous linear elastic material. Equation of motion in terms of Lame constants is first derived from field equations of elasticity, and then solved analytically with the help of Bessel’s functions. For each classical possible boundary condition the characteristic free vibration equation is presented in closed forms. After verifying the present results with the available literature a parametric study is conducted. Variation of the dimensionless natural frequencies with respect to the boundary conditions and the cylinder aspect ratio outer radius/inner radius is illustrated graphically and some numerical results are given in tabular form

Anahtar Kelimeler

Free Vibration Natural frequency Cylindrical Bessel Functions Analitical Solution

Kaynakça

  • Chree C. The Equations of an Isotropic Elastic Solid in Polar and Cylindrical Coordinates. Their Solutions and Applications. Transactions of the Cambridge Philosophical Society, 1889; 14: 250–309.
  • Greenspon J.E. Flexural Vibrations of a Thick-Walled Circular Cylinder According to the Exact Theory of Elasticity. Journal of Aero/Space Sciences, 1957; 27: 1365–1373.
  • Gladwell G.M., Tahbildar U.C. Finite Element Analysis of Axisymmetric Vibrations of Cylinders. Journal of Sound and Vibration, 1972; 22: 143–157.
  • Hutchinson J.R. Vibrations of Solid Cylinders. Journal of Applied Mechanics, 1980; 47: 901–907.
  • Hutchinson J.R., El-Azhari S.A. Vibrations of Free Hollow Circular Cylinders. Journal of Applied mechanics, 1986; 53: 641–646.
  • Singal R.K., Williams K.A. Theoretical and Experimental Study of Vibrations of Thick Circular Cylindrical Shell and Rings. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1988; 110: 533–537.
  • Ghosh A.K. Axisymmetric Vibration of a Long Cylinder. Journal of Sound and Vibration, 1995; 186(5): 711–721.
  • Gazis D.C. Three Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinder. Journal of the Acoustical Society of America, 1959; 31: 568–578.
  • Leissa A.W., So J. Accurate Vibration Frequencies of Circular Cylinders from Three- Dimensional analysis. Journal of the Acoustical Society of America, 1995; 98: 2136–2141.
  • So J., B Leissa A.W. Free Vibration of Thick Hollow Circular Cylinders from Three- Dimensional analysis. Journal of Vibration and Acoustics, 1997; 119: 89–95.
  • Liew K.M., Hung K.C., Lim M.K. Vibration of Stress Free Hollow Cylinders of Arbitrary Cross-Section. Journal of Applied Mechanics, ASME, 1995; 62: 718–724.
  • Hung K.C., Liew K.M., Lim M.K. Free Vibration of Cantilevered Cylinders: Effects of Cross-Sections and Cavities. Acta Mechanica, 1995; 113: 37–52.
  • Zhou D., Cheung Y.K., Lo S.H., Au F.T.K. 3D Vibration Analysis of Solid and Hollow Circular Cylinders via Chebyshev–Ritz Method. Computer Methods in Applied Mechanics and Engineering, 2003; 192: 1575–1589.
  • Gladwell G.M., Vijay D.K. Natural Frequencies of Free Şnite Length Circular Cylinders. Journal of Sound and Vibration, 1975; 42: 387–397.
  • Wang H., Williams K. Vibrational Modes of Thick Cylinders of Şnite Length. Journal of Sound and Vibration, 1996; 191: 1996, 955–971.
  • Mofakhami M.R., Toudeshky H.H., Hashemi Sh. H. Finite Cylinder Vibrations with Different End Boundary Conditions. Journal of Sound and Vibration, 2006; 297: 293–314.
  • Yıldırım V. Heat-Induced, Pressure-Induced and Centrifugal-Force-Induced Exact Axisymmetric Thermo-Mechanical Analyses in a Thick-Walled Spherical Vessel, an Infinite Cylindrical Vessel, and a Uniform Disk Made of an Isotropic and Homogeneous Material.
  • International Journal of Engineering & Applied Sciences (IJEAS), 2017; 9(2): 66-87. http://dx.doi.org/10.24107/ijeas.309786
  • Watson G.N., “A Treatise on the Theory of Bessel Functions”, Cambridge University Press, 1922.
  • Bowman. F., “Introduction to Bessel Functions”, New York: Dover, 1958.
  • Hildebrand F.B., “Advanced Calculus for Applications”, Prentice-Hall. Inc. Englewood Cliffs, New Jersey, 1962.
  • Abramowitz M., Stegun I.A. (Eds.)., “Handbook of Mathematical Functions with Formulas, Graphs and mathematical tables”, 9th printing, New York, Dover, 1972.
  • Keleş İ., Tütüncü N. Exact Analysis of Axisymmetric Dynamic Response of Functionally Graded Cylinders (or Disks) and Spheres”, Journal of Applied Mechanics, 2011; 78(6): 061014 (7 pages).
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Araştırma Makaleleri
Yazarlar

Vebil Yıldırım Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2019
Yayımlandığı Sayı Yıl 2019 Sayı: 15

Kaynak Göster

APA Yıldırım, V. (2019). KALIN CİDARLI İÇİ BOŞ SİLİNDİRLERİN DOĞAL FREKANSLARININ DIŞ/İÇ ÇAP ORANI VE SINIR ŞARTLARI İLE DEĞİŞİMİ. GİDB Dergi(15), 3-12.

88x31.png

Bu site ve içerisinde yayınlanan eserler Creative Commons AI 4.0 Uluslararası Lisansı ile lisanslanmıştır.
GiDB|DERGi, İstanbul Teknik Üniversitesi tarafından yayınlanmaktadır.