Browse > Article
http://dx.doi.org/10.12989/sem.2015.54.3.419

AMDM for free vibration analysis of rotating tapered beams  

Mao, Qibo (School of Aircraft Engineering, Nanchang HangKong University)
Publication Information
Structural Engineering and Mechanics / v.54, no.3, 2015 , pp. 419-432 More about this Journal
Abstract
The free vibration of rotating Euler-Bernoulli beams with the thickness and/or width of the cross-section vary linearly along the length is investigated by using the Adomian modified decomposition method (AMDM). Based on the AMDM, the governing differential equation for the rotating tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and the closed form series solution of the corresponding mode shapes can be easily obtained simultaneously. The computed results for different taper ratios as well as different offset length and rotational speeds are presented in several tables and figures. The accuracy is assured from the convergence and comparison with the previous published results. It is shown that the AMDM provides an accurate and straightforward method of free vibration analysis of rotating tapered beams.
Keywords
adomian modified decomposition method; rotating tapered beam; taper ratio; natural frequency; mode shape;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Adomian, G. (1994), Solving frontier problems of physics: The decomposition method, Kluwer-Academic Publishers, Boston.
2 Banerjee, J.R. (2000), "Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method", J. Sound Vib., 233(5), 857-875.   DOI
3 Banerjee, J.R., Su, H. and Jackson, D.R. (2006), "Free vibration of rotating tapered beams using the dynamic stiffness method", J. Sound Vib., 298, 1034-1054.   DOI
4 Banerjeea, J.R. and Jackson, D.R. (2013), "Free vibration of a rotating tapered Rayleigh beam: A dynamic stiffness method of solution", Comput. Struct., 124, 11-20.   DOI
5 Bazoune, A. (2007), "Effect of tapering on natural frequencies of rotating beams", Shock Vib., 14, 169-179.   DOI
6 Hsu, J.C., Lai, H.Y. and Chen, C.K. (2008), "Free vibration of non-uniform Euler-Bernoulli beams with general elastically end constraints using Adomian modified decomposition method", J. Sound Vib., 318, 965-981.   DOI   ScienceOn
7 Mao, Q. (2011), "Free vibration analysis of multiple-stepped beams by using Adomian decomposition method", Math. Comput. Model., 54 (1-2), 756-764.   DOI   ScienceOn
8 Mao, Q. (2012), "Free vibration analysis of elastically connected multiple-beams by using the Adomian modified decomposition method", J. Sound Vib., 331, 2532-2542.   DOI
9 Mao, Q. and Pietrzko, S. (2012), "Free vibration analysis of a type of tapered beams by using Adomian decomposition method", Appl. Math. Comput. 219(6), 3264-3271.   DOI
10 Mao, Q. (2013), "Application of Adomian modified decomposition method to free vibration analysis of rotating beams", Math. Probl. Eng., Article ID 284720, doi: 10.1155/2013/284720.   DOI
11 Ozdemir, O. and Kaya, M.O. (2006a), "Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method", J. Sound Vib., 289, 413-420.   DOI
12 Ozdemir, O. and Kaya, M.O. (2006b), "Flapwise bending vibration analysis of double tapered rotating Euler- Bernoulli beam by using the differential transform method", Meccanica, 41, 661-670.   DOI
13 Rajasekaran, S. (2013), "Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams", Int. J. Mech. Sci., 74, 15-31.   DOI
14 Rach, R., Adomian, G. and Meyers, R.E. (1992), "A modified decomposition", Comput. Math. Appl., 23, 17-23.   DOI
15 Vinod, K.G., Gopalakrishnan, S. and Ganguli, R. (2007), "Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements", Int. J. Solids Struct., 44(18-19), 5875-5893.   DOI
16 Wang, G. and Wereley, N.M. (2004), "Free vibration analysis of rotating blades with uniform tapers", AIAA J., 42(12), 2429-2437.   DOI