References
- Al-Ansary, M.D. (1998), "Flexural vibrations of rotating beams considering rotary inertia", Comput. Struct., 69, 321-328. https://doi.org/10.1016/S0045-7949(98)00134-5
- ALGOR V. 20.3. (2007), Linear Mode Shapes and Natural Frequencies with Load Stiffening Module.
- Banerjee, J.R. (2000), "Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method", J. Sound Vib., 233, 857-875. https://doi.org/10.1006/jsvi.1999.2855
- Banerjee, J.R. (2001), "Dynamic stiffness formulation and free vibration analysis of centrifugally stiffened Timoshenko beam", J. Sound Vib., 247, 97-115. https://doi.org/10.1006/jsvi.2001.3716
- Bellman, R. and Casti, J. (1971), "Differential quadrature and long-term integration", J. Math. Anal. Appl., 34, 235-238. https://doi.org/10.1016/0022-247X(71)90110-7
- Bellman, R.E. and Roth, R.S. (1986), Methods in Approximation: Techniques for Mathematical Modeling, Editorial D. Reidel Publishing Company, Dordrecht, Holland.
- Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: A review", Appl. Mech. Rev., 49, 1-28. https://doi.org/10.1115/1.3101882
- Choi, S.T., Wu, J.D. and Chou, Y.T. (2000), "Dynamic analysis of a spinning Timoshenko beam by the differential quadrature method", AIAA J., 38, 851-856. https://doi.org/10.2514/2.1039
- Chung, J. and Yoo, H.H. (2002), "Dynamic analysis of a rotating cantilever beam by using the finite element method", J. Sound Vib., 249, 147-164. https://doi.org/10.1006/jsvi.2001.3856
- Du, H., Lim, M.K. and Liew, K.M. (1994), "A power solution for vibration of a rotating Timoshenko beam", J. Sound Vib., 175, 505-523. https://doi.org/10.1006/jsvi.1994.1342
- Gunda, J.B. and Ganguli, R. (2008), "Stiff-string basis functions for vibration analysis of high speed rotating beams", J. Appl. Mech. - T. ASME, 75(2), 0245021-0245025.
- Gunda, J.B. and Ganguli, R. (2008), "New rational interpolation functions for finite element analysis of rotating beams", Int. J. Mech. Sci., 50, 578-588. https://doi.org/10.1016/j.ijmecsci.2007.07.014
- Gunda, J.B., Gupta, R.K. and Ganguli, R. (2009), "Hybrid stiff-string-polynomial basis functions for vibration analysis of high speed rotating beams", Comput. Struct., 87(3-4), 254-265. https://doi.org/10.1016/j.compstruc.2008.09.008
- Gunda, J.B., Singh, A.P., Chhabra, P.S. and Ganguli, R. (2007), "Free vibration analysis of rotating tapered blades using Fourier-p superelement", Struct. Eng. Mech., 27(2), 243-257. https://doi.org/10.12989/sem.2007.27.2.243
- Hodges, D.H. and Rutkowski, M.J. (1981), "Free vibration analysis of rotating beams by a variable order finite method", AIAA J., 19(11), 1459-1466. https://doi.org/10.2514/3.60082
- Karami, G., Malekzadeh, P. and Shahpari, S.A. (2003), "DQEM for vibration of shear deformable nonuniform beams with general boundary conditions", Eng. Struct., 25, 1169-1178. https://doi.org/10.1016/S0141-0296(03)00065-8
- Kumar, A. and Ganguli, R. (2009), "Rotating Beams and Nonrotating Beams with Shared Eigenpair", J. Appl. Mech., 76(5) Article Number: 051006 (14 pages).
- Laura, P.A.A. and Gutiérrez, R.H. (1993), "Analysis of vibrating Timoshenko beams using the method of differential quadrature", Shock Vib. Digest, 1, 9-93.
- Lee, S.Y. and Sheu, J.J. (2007), "Free vibration of an extensible rotating inclined Timoshenko beam", J. Sound Vib., 304(3-5), 606-624. https://doi.org/10.1016/j.jsv.2007.03.005
- Lin, S.C. and Hsiao, K.M. (2001), "Vibration analysis of a rotating Timoshenko beam", J. Sound Vib., 240, 303- 322. https://doi.org/10.1006/jsvi.2000.3234
- Liu, G.R. and Wu, T.Y. (2001), "Vibration analysis of beams using the generalized differential quadrature rule and domain decomposition", J. Sound Vib., 246(3), 461-481. https://doi.org/10.1006/jsvi.2001.3667
- Mei, C. (2008), "Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam", Comput. Struct., 86, 1280-1284. https://doi.org/10.1016/j.compstruc.2007.10.003
- Naguleswaran, S. (1994), "Lateral vibration of a centrifugally tensioned uniform Euler-Bernoulli beam", J. Sound Vib., 176(5), 613-624. https://doi.org/10.1006/jsvi.1994.1402
- Ouyang, H. and Wang, M. (2007), "A dynamic model for a rotating beam subjected to axially moving forces", J. Sound Vib., 308(3-5), 674-682. https://doi.org/10.1016/j.jsv.2007.03.082
- Rao, S.S. and Gupta, R.S. (2001), "Finite element vibration analysis of rotating Timoshenko beams", J. Sound Vib., 242(1), 103-124. https://doi.org/10.1006/jsvi.2000.3362
- Senatore, A. (2006), "Measuring the natural frequencies of centrifugally tensioned beam with laser doppler vibrometer", Measurement, 39, 628-633. https://doi.org/10.1016/j.measurement.2006.01.006
- Seon Han, M., Benaroya, H. and Wei, T. (1999), "Dynamics of transversely vibrating beams using four engineering theories", J. Sound Vib., 225, 935-988. https://doi.org/10.1006/jsvi.1999.2257
- Shu, C. and Chen, W. (1999), "On optimal selection of interior points for applying discretized boundary conditions in DQ vibration analysis of beams and plates", J. Sound Vib., 222(2), 239-257. https://doi.org/10.1006/jsvi.1998.2041
- Shu, C. (2000), Differential Quadrature and Its Application in Engineering. Editorial Springer-Verlag London Limited, Great Britain.
- Singh, A.P., Mani, V. and Ganguli, R. (2007) "Genetic programming metamodel for rotating beams", CMES - Comput. Model. Eng. Sci., 21(2), 133-148.
- Vinod, K.G., Gopalakrishnan, S. and Gangul, R. (2007), "Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements", Int. J. Solids Struct., 44, 5875-5893. https://doi.org/10.1016/j.ijsolstr.2007.02.002
- Yoo, H.H. and Shin, S.H. (1998), "Vibration analysis of rotating cantilever beams", J. Sound Vib., 212(5), 807- 828. https://doi.org/10.1006/jsvi.1997.1469
- Wolfram, S. (1996), Mathematica: A System for Doing Mathematics by Computer. Third Ed. Addison-Wesley.
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