DAİRE EKSENLİ ÇUBUKLARIN SERBEST TİTREŞİMİNİ ETKİLEYEN FAKTÖRLERİN İNCELENMESİ

Bu çalışmada daire eksenli çubukların serbest titreşimini etkileyen faktörler incelenmiştir. Daire eksenli çubukların serbest titreşimini idare eden diferansiyel denklemler Timoshenko kiriş teorisi kullanılarak elde edilmiştir. Çubuk malzemesi homojen, izotropik ve lineer elastik olarak kabul edilmiştir. Taşıma matrisi yöntemi yardımı ile problemin eleman dinamik rijitlik matrisi elde edilmektedir. Taşıma matrisi seri açılımı yapılarak elde edilmiş, hassasiyetin artırılması için Cayley-Hamilton prensibi kullanılmıştır. Elde edilen dinamik rijitlik matrisinin karakteristik polinomunun kökleri problemin serbest titreşim frekanslarını vermektedir. Farklı narinlik oranları ve açılara sahip daire eksenli çubukların serbest titreşim frekanslarına etkisi araştırılmıştır. Elde edilen sonuçların literatür ile uyumlu olduğu görülmektedir.

INVESTIGATION OF THE FACTORS AFFECTING THE FREE VIBRATION OF CIRCULAR RODS

In this study the elements affecting the free vibration of circular rods are investigated. The governing differential equations of the free vibration of circular rods are obtained by the Timoshenko beam theory. Material of the rod is assumed to be homogeneous, isotropic and linear elastic. The element dynamic stiffness matrices are calculated via the transfer matrix method. The transfer matrix is determined by series expansion and the precision is increased with the Cayley-Hamilton principal. Roots of the characteristic function of the dynamic stiffness matrix gives the natural free vibration frequencies. The effect of various slenderness ratios and axis opening angles on the natural frequencies are investigated. The results are consistent with the literature.

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[1] M. HAJİANMALEKI AND M. S. QATU, “Vibrations of straight and curved composite beams: A review,” Composite Structures. 2013.
[2] W. B. BİCKFORD AND B. T. STROM, “Vibration of plane curved beams,” J. Sound Vib., 1975.
[3] T. IRİE, G. YAMADA, AND K. TANAKA, “Natural frequencies of out-of-plane vibration of arcs,” J. Appl. Mech., vol. 49, no. 4, pp. 910–913, 1982.
[4] T. IRİE, G. YAMADA, AND K. TANAKA, “Natural frequencies of in-plane vibration of arcs,” ASME, Trans. J. Appl. Mech., vol. 50, pp. 449–452, 1983.
[5] B. TABARROK, A. N. SİNCLAİR, M. FARSHAD, AND H. Yİ, “On the dynamics of spatially curved and twisted rods-A finite element formulation,” J. Sound Vib., 1988.
[6] K. KANG, C. W. BERT, AND A. G. STRİZ, “Vibration analysis of shear deformable circular arches by the differential quadrature method,” J. Sound Vib., vol. 183, no. 2, pp. 353–360, 1995.
[7] A. A. KHDEİR AND J. N. REDDY, “Free and forced vibration of cross-ply laminated composite shallow arches,” Int. J. Solids Struct., 1997.
[8] V. YİLDİRİM, “A computer program for the free vibration analysis of elastic arcs,” Comput. Struct., 1997.
[9] V. YİLDİRİM, “Rotary inertia, axial and shear deformation effects on the in-plane natural frequencies of symmetric cross-ply laminated circular arches,” J. Sound Vib., 1999.
[10] V. YİLDİRİM, “Common effects of the rotary inertia and shear deformation on the out-of-plane natural frequencies of composite circular bars,” Compos. Part BEngineering, 2001.
[11] E. TÜFEKÇİ, “Exact Solution Of Free In-plane Vibration Of Shallow Circular Arches,” Int. J. Struct. Stab. Dyn., 2001.
[12] W. P. HOWSON AND A. K. JEMAH, “Exact Out-of-Plane Natural Frequencies of Curved Timoshenko Beams,” J. Eng. Mech., 2002.
[13] E. TUFEKCİ AND O. Y. DOGRUER, “Out-of-plane free vibration of a circular arch with uniform cross-section: Exact solution,” J. Sound Vib., 2006.
[14] E. VİOLA, M. DİLENA, AND F. TORNABENE, “Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches,” J. Sound Vib., 2007.
[15] F. F. ÇALIM AND F. G. AKKURT, “Static and free vibration analysis of straight and circular beams on elastic foundation,” in Mechanics Research Communications, 2011.
[16] F. F. ÇALIM, N. KARACA, AND H. T. TÜRKER, “Out-of-Plane Free Vibrations of Circular Rods,” World Acad. Sci. Eng. Technol. Int. J. Mech. Aerospace, Ind. Mechatron. Manuf. Eng., vol. 9, no. 5, pp. 812–815, 2015.
[17] M. İNAN, Elestomekanikte başlangıç değerleri metodu ve taşıma matrisi. TC İstanbul Teknik Üniversitesi Kütüphanesi, İstanbul, Türkiye, 1964.