Vol. 12, No. 1, pp. 55-65 (2016)
A NUMERICAL METHOD FOR FREE VIBRATION OF
AXIALLY LOADED COMPOSITE TIMOSHENKO BEAM
Aleksandar Prokić * , Miroslav T. Bešević and Martina Vojnić-Purčar
Faculty of Civil Engineering, University of Novi Sad, Kozaračka 2a, 24000 Subotica, Serbia
*(Corresponding author: E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it. )
Received: 13 February 2014; Revised: 17 December 2014; Accepted: 14 January 2015
DOI:10.18057/IJASC.2016.12.1.5
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ABSTRACT
In this paper, a numerical method is employed to study the free vibration of axially loaded composite Timoshenko beam. The problem is governed by a set of coupled second-order ordinary differential equations of motion, under different boundary conditions. The method is based on numerical integration rather than the numerical differentiation since the highest derivatives of governing functions are chosen as the basic unknown quantities. The kernels of integral equations turn out to be Green's function of corresponding equation with homogeneous boundary conditions. The accuracy of the proposed method is demonstrated by comparing the calculated results with those available in the literature. It is shown that good accuracy can be obtained even with a relatively small number of nodes.
KEYWORDS
Numerical method, Green’s function, Vibration, Timoshenko beam, Integral equations
REFERENCES
[1] Ansari, R., Gholami, R. and Hosseini, K., "A Sixth-order Compact Finite Difference Method for Free Vibration Analysis of Euler-Bernoulli Beams", Mathematical Sciences, 2011, Vol. 5, No. 4, pp.307-320.
[2] Banerjee, J.R., "Dynamic Stiffness Formulation and Free Vibration Analysis of Centrifugally Stiffened Timoshenko Beams", Journal of Sound and Vibration, 2001, Vol. 247, No. 1, pp.97–115.
[3] Banerjee, J.R., Su, H. and Jayatunga, C., "A Dynamic Stiffness Element for Free Vibration Analysis of Composite Beams and Its Application to Aircraft Wings", Computers and Structures, 2008, Vol. 86, No. 6, pp.573–579.
[4] Berczynski, S. and Wroblewski T., "Vibration of Steel-Concrete Composite Beams Using the Timoshenko Beam Model", Journal of Vibration and Control, 2005, Vol. 11, No. 6, pp.829–848.
[5] Biscontin, G., Morassi A. and Wendel, P., "Vibrations of Steel-Concrete Composite Beams", Journal of Vibration and Control, 2000, Vol. 6, No. 5, pp.691–714.
[6] Borbón, F., Mirasso, A. and Ambrosini, D., "A Beam Element for Coupled Torsional-flexural Vibration of Doubly Unsymmetrical Thin Walled Beams Axially Loaded", Computers and Structures, 2011, Vol. 89, No. 13-14, pp.1406–1416.
[7] Byron, F.W. and Fuller, R.W., “Mathematics of Classical and Quantum Physics“, Dover Publications, Inc., New York, 1992.
[8] Fu-le, L. and Zhi-zhong, S., "A Finite Difference Scheme for Solving the Timoshenko Beam Equations with Boundary Feedback", Journal of Computational and Applied Mathematics, 2007, Vol. 200, No. 2, pp.606- 627.
[9] Hajdin, N., "A Method for Numerical Solution of Boundary Value Problems", Trans. Civ. Engng. Dept,. 1958, No. 4, pp.1-58.
[10] Kaya, M.O. and Ozgumus Ozdemir, O., "Flexural-torsional-coupled Vibration Analysis of Axially Loaded Closed-section Composite Timoshenko Beam by Using DTM", Journal of Sound and Vibration, 2007, Vol. 306, No. 3-5, pp.495–506.
[11] Li J., Shen, R., Hua, H. and Jin, X., "Bending–torsional Coupled Dynamic Response of Axially Loaded Composite Timoshenko Thin-walled Beam with Closed Crosssection", Composite Structures, 2004, Vol. 64, No. 1, pp.23–35.
[12] Liu, Z., Yin, Y., Wang, F., Zhao, Y. and Cai, L., "Study on Modified Differential Transform Method for Free Vibration Analysis of Uniform Euler-Bernoulli Beam", Structural Engineering and Mechanics, An Int'l Journal, 2013, Vol. 48, No. 5, pp.697-709.
[13] Mirtalaie, S.H., Mohammadi, M., Hajabasi, M.A. and Hejripour F., "Coupled Lateral-torsional Free Vibrations Analysis of Laminated Composite Beam using Differential Quadrature Method", Word Academy of Science, Engineering and Technology, 2012, No. 67, pp.117-122.
[14] Pagani, A., Boscolo, M., Banerjee, J.R. and Carrera, E., "Exact Dynamic Stiffness Elements Based on One-dimensional Higher-order Theories for Free Vibration Analysis of Solid and Thin-walled Structures", Journal of Sound and Vibration, 2013, Vol. 332, No. 23, pp.6104-6127.
[15] Pan, D., Chen, G. and Lou, M., "A Modified Modal Perturbation Method for Vibration Characteristics of Non-prismatic Timoshenko Beams", Structural Engineering and Mechanics, An Int'l Journal, 2011, Vol. 40, No. 5, pp.689-703.
[16] Rajasekaran, S., "Free Vibration of Centrifugally Stiffened Axially Functionally Graded Tapered Timoshenko Beams Using Differential Transformation and Quadrature Methods", Applied Mathematical Modelling, 2013, Vol. 37, No. 6, pp.440-4463.
[17] Reddy, J.N., "On Locking-free Shear Deformable Beam Finite Elements", Comput. Methods Appl. Mech. Engrg., 1997, Vol. 149, pp.113-132.
[18] Vo, T.P., Lee, J. and Lee, K., "On Triply Coupled Vibrations of Axially Loaded Thin-walled Composite Beams", Computers and Structures, 2010, Vol. 88, No. 3-4, pp.144–153.