VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL  DISTRIBUTION PROPERTIES

Özge ÖZDEMİR

VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES

Özge ÖZDEMİR

Öz

In this study, vibration characteristics of functionally graded rotating Timoshenko beams that undergoes flapwise bending vibration are analysed. Beam models with different material distribution properties are considered. The energy expressions are derived by introducing several explanotary figures and tables. Applying the Hamilton’s Principle to the derived energy expressions, governing differential equations of motion and the boundary conditions are obtained. Related formulation is coded by using MATLAB and in the solution part, the equations of motion, including the parameters for the rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM). Natural frequencies of the modeled beams are obtained and the effects of rotational speed and material distribution on the vibrational characteristics of the beam are investigated. Obtained results are distributed in several tables.

Anahtar Kelimeler

Differential Transform Method; Functionally Graded Beam; Rotating Timoshenko Beam

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Referanslar

Akash, B. A., Mamlook, R., Mohsen, S. M., 1999, “Multi-criteria selection of electric power plants using analytical hierarchy process”, Electric Power Systems Research, Cilt 52, Sayı 1, ss. 29-35.

Alshorbagy AE, Eltaher MA, Mahmoud FF, 2011, Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35, 412–425.

Bhimaraddi A, Chandrashekhara K., 1991, Some observation on the modeling of laminated composite beams with general lay-ups, Composite Structures, 19, 371–380

Chakraborty A, Gopalakrishnan S, Reddy JN., 2003, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanical Sciences, 45, 519–539.

Dadfarnia M., 1997, Nonlinear forced vibration of laminated beam with arbitrary lamination, M.Sc. Thesis, Sharif University of Technology.

Deng HD and Wei C, 2016, Dynamic characteristics analysis of bi-directional functionally graded Timoshenko beams, Composite Structures, in press.

Eringen, AC., 1980, Mechanics of Continua, Robert E. Krieger Publishing Company, Huntington, New York.

Giunta G, Crisafulli D, Belouettar S, Carrera E., 2011, Hierarchical theories for the free vibration analysis of functionally graded beams, Composite Structures, 94, 68–74.

Hodges, D. H., Dowell, E. H., 1974, Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades, NASA Technical Report,NASA TN D-7818.

Huang Y, Li XF., 2010, A new approach for free vibration of axially functionally graded beams with non-uniform cross-section, Journal of Sound and Vibration, 329, 2291–2303.

Kapuria S, Bhattacharyya M, Kumar AN., 2008, Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation, Composite Structures, 82, 390–402.

Kaya, M.O., Ozdemir Ozgumus, O., 2007, Flexural–torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM, Journal of Sound and Vibration, 306, 495–506.

Kaya, M.O., Ozdemir Ozgumus, O., 2010, Energy expressions and free vibration analysis of a rotating uniform timoshenko beam featuring bending–torsion coupling, Journal of Vibration and Control, 16(6), 915–934.

Kollar, LR., Springer, GS., 2003, Mechanics of Composite Structures. Cambridge University Press, United Kingdom.

Lai SK, Harrington J, Xiang Y, Chow KW., 2012, Accurate analytical perturbation approach for large amplitude vibration of functionally graded beams, International Journal of Non-Linear Mechanics, 47, 473–480.

Li XF., 2008, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli Beams, Journal of Sound and Vibration, 318, 1210–1229.

Li XF, Kang YA, Wu JX, 2013, Exact frequency equation of free vibration of exponentially funtionally graded beams, Applied Acoustics, 74 (3), 413-420.

Loja MAR, Barbosa JI, Mota Soares CM., 2012, A study on the modelling of sandwich functionally graded particulate composite, Composite Structures, 94, 2209–2217.

Loy C.T., Lam K.Y., Reddy J.N., 1999, Vibration of functionally graded cylinderical shells, International Journal of Mechanical Science, 41, 309-324.

Lu CF, Chen WQ., 2005, Free vibration of orthotropic functionally graded beams with various end conditions, Structural Engineering and Mechanics, 20, 465–476.

Ozdemir O., 2016, Application of The Differential Transform Method to The Free Vibration Analysis of Functionally Graded Timoshenko Beams, Journal of Theoretical and Applied Mechanics 54, 4, 1205-1217.

Ozdemir Ozgumus, O., Kaya, M.O., 2013, Energy expressions and free vibration analysis of a rotating Timoshenko beam featuring bending–bending-torsion coupling, Archive of Applied Mechanics, 83, 97–108.

Sina S.A., Navazi H.M., Haddadpour H., 2009, An analytical method for free vibration analysis of functionally graded beams, Materials and Design, 30, 741–747.

Şimsek M., 2010, Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories, Nuclear Engineering and Design, 240, 697–705.

Tang AY, Wu JX, Li XF and Lee KY, 2014, Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams, International Journal of Mechanical Sciences, 89, 1-11.

Thai HT, Vo TP., 2012, Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories, International Journal of Mechanical Sciences, 62, 57–66.

Wang Z., Wang X., Xu G., Cheng S. and Zeng T., 2016, Free vibration of two directional functionally graded beams, Composite Structures, 135, 191-198.

Wattanasakulpong N, Prusty BG, Kelly DW, Hoffman M., 2012, Free vibration analysis of layered functionally graded beams with experimental validation, Materials & Design, 36, 182–190.

Zhong Z, Yu T., 2007, Analytical solution of a cantilever functionally graded beam, Composites Science and Technology, 67, 481–488.