Multi-step Diferansiyel Transform Metodu ile Uç Kütle Eklentili Kirişlerin Serbest Titreşim Analizi

Hilal Doğanay Katı, Hakan Gökdağ
410 47

Öz


Kiriş-uç kütle sistemlerinin dinamik analizi robot kolları ve manipulatörler gibi mekanik sistemlerin başarılı bir şekilde tasarlanması açısından oldukça önemlidir. Literatürdeki birçok çalışmada bu sistemlerin serbest titreşimini analitik olarak çözümlemek için az sayıda değişken kesitli kiriş modeli dikkate alınmış, çoğunlukla sabit kesitli kiriş modeli kullanılmıştır. Ayrıca, uç kütlenin noktasal olduğu, kiriş ve uç kütle koordinat merkezlerinin çakışık olduğu kabul edilmiştir. Mevcut çalışmada burulmaya ve iki farklı düzlemde eğilmeye maruz, kiriş ve uç kütle merkezlerinin çakışık olmadığı bir sistem ele alınmış ve serbest titreşim analizi için yarı-nümerik yöntem olan Multi-Step Diferansiyel Transform Metodu (MDTM) uygulanmıştır. Sistemin doğal frekansları ve mod şekilleri iki farklı sınır şartı (ankastre ve serbest) için elde edilmiştir. Ayrıca, kiriş uzunluğu, uç kütle boyutları, kesit daralma oranı (taper ratio) gibi parametrelerin doğal frekanslar üzerindeki etkisi incelenmiştir. Elde edilen sonuçların doğruluğu yaygın bir şekilde kullanılan sonlu eleman yazılımı (ANSYS) ile karşılaştırılmış ve yeterince uyumlu olduğu gözlenmiştir.


Anahtar kelimeler


DTM ve Multi-Step DTM, Titreşim, Euler-Bernoulli Kirişi, Doğal Frekanslar ve Mod şekilleri, ANSYS

Tam metin:

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Referanslar


. Boyce W.E., Handelman G.H., Vibration of rotating beams with tip mass, Journal of Zeitschrift für angewandte Mathematik und Physik ZAMP, 12(5), 369-392, 1961.

Craig R R., Rotating Beam with Tip Mass Analyzed by a Variational Method, Journal of the Acoustical Society of America, 35(7), 990, 1963.

Gürgöze M., Özgür K., Erol H., On the Frequencies of a Cantilevered Beam with a Tip Mass and In-Span Support, 56(1), 85-92, 1995.

Gürgöze M., On the Eigenfrequencies of a Cantilever Beam with Attached Tip Mass and a Spring-Mass System, Journal of Sound and Vibration, 190(2), 149-162, 1996.

Mabie H.H., Rogers C.B., Transverse Vibrations of Tapered Cantilever Beam with End Loads, Journal of the Acoustical Society of America, 36(3), 463, 1964.

Kuo Y.H., Wu T.H., Lee S.Y., Bending Vibrations of a Rotating Non-Uniform Beam with Tip Mass and an Elastically Restrained Root, 42(2), 229-236, 1992.

Auciello N.M., Transverse Vibrations of a Linearly Tapered Cantilever Beam with Tip Mass of Rotatory Inertia and Eccentricity, Journal of Sound and Vibration, 194(1), 25-34, 1996.

Auciello N.M., Nole G., Vibrations of a Cantilever Tapered Beam with Varying Section Properties and Carrying a Mass at the free end, Journal of Sound and Vibration, 214(1), 105-119, 1998.

Auciello N.M., Free Vibration of a Restrained Shear-Deformable Tapered Beam with a Tip Mass at its Free End, 237(3), 542-549, 2000.

Wu J-S., Chen C-T., An Exact Solution for the Natural Frequencies and Mode Shapes of an Immersed Elastically Restrained Wedge Beam Carrying an Eccentric Tip Mass Moment of Inertia, Journal of Sound and Vibration, 286, 549-568, 2005.

Boiangiu M., Ceausu V., Untariou C.D., A Transfer Matrix Method for Free Vibration Analysis of Euler-Bernoulli Beams with Variable Cross Section, Journal of Vibration of Control, 22(11), 2591-2602, 2014.

Yang K.Y., The Natural Frequencies of a Non-Uniform Beam with a Tip Mass and With Translational and Rotational Springs, Journal of Sound and Vibration, 137(2), 339-341, 1990.

Tang H-L., Shen Z-B., Li D-K., Vibration of nonuniform carbon nanotube with attached mass via nonlocal Timoshenko beam theory, 28(9), 3741-3747, 2014.

Hoa S.V., Vibration of a Rotating Beam with Tip Mass, Journal of Sound and Vibration, 67(3), 369-381, 1979.

Oguamanam D.C.D., Free Vibration of Beams with Finite Mass Rigid Tip Load and Flexural-Torsional Coupling, International Journal of Mechanical Science, 45, 963-979, 2003.

Gökdağ H., Kopmaz O., Coupled Bending and Torsional Vibration of a Beam with in-span and tip attachments, Journal of Sound and Vibration, 287, 591-610, 2005.

Oguamanam, D.C.D., Arshad, M., On the natural frequencies of a flexible manipulator with a tip load, Proceedings of the Institution of Mechanical Engineers, 219, 1199-1205, 2005.

Salarieh H., Ghorashi M., Free Vibration of Timoshenko Beam with Finite Mass Rigid Tip Load and Flexural-Torsional Coupling, International Journal of Mechanical Science, 48, 763-779, 2006.

Vakil M., Sharbati E., Vakil A., Heidari F., Fotouhi R., Vibration analysis of a Timoshenko beam on a moving base, Journal of Vibration and Control, 21(6), 1068-1085, 2013.

Ansari M., Esmailzadeh E., Jalili N., Coupled vibration and parameter sensitivity analysis of rocking-mass vibrating gyroscopes, Journal of Sound and Vibration, 327, 564-583, 2009.

Ansari M., Esmailzadeh E., Jalili N., Exact Frequency Analysis of a Rotating Cantilever Beam With Tip Mass Subjected to Torsional-Bending Vibrations, Journal of Vibration and Acoustics, 133(4), 041003, 2011.

Pukhov, G.E., Expansion formulas for differential transforms. Cybern Syst. Anal. 17, 460-464, 1981.

Pukhov, G.E., Differential transforms and circuit theory. Int. J. Circ. Theor. App. 10, 265-276, 1982.

Zhou, J.K., Differential Transformation and Its Applications for Electrical Circuits. Huazhong University Press. Wuhan China, 1986.

Yesilce, Y., Determination of natural frequencies and mode shapes of axially moving Timoshenko beams with different boundary conditions using differential transform method. Adv. Vib. Eng. 12(1), 90-108, 2013.

Yesilce, Y., Differential transform method and numerical assembly technique for free vibration analysis of the axial-loaded Timoshenko multi-step beam carrying a number of intermediate lumped masses and rotary inertias. Structural Engineering and Mechanics. 53(3), 537-573, 2015.

Rajasekaran, S., Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams. International Journal of Mechanical Science. 74, 15-31, 2013.

Rashidi, M.M., Chamkha, A.J., Keimanesh, M., Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet. American Journal of

Computational Mathematics. 6, 119-128, 2011.

Liu, B., Zhou, X., Du, Q., Differential Transform Method for Some Delay Differential Equations, Applied Mathematics. 6, 585-593, 2015.




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