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Rui, Xiaoting; Wang, Guoping; Lu, Yuqi; Yun, Laifeng

Transfer matrix method for linear multibody system. (English) Zbl 1181.70010

Multibody Syst. Dyn. 19, No. 3, 179-207 (2008).
The authors present a new method for obtaining the dynamic characteristics of linear multibody systems. The method is a generalization of the traditional transfer matrix method. It is claimed that the method is computationally efficient and applicable to linear flexible and linear hybrid multibody systems. The authors present a detailed algorithm together with a flowchart for their method. They also provide a helpful illustrative example. The paper should be of interest and use to design engineers concerned with the characteristics of large flexible dynamical systems.
Reviewer: Ronald L. Huston (Cincinnati)

Cited in 12 Documents

MSC:

70E55 Dynamics of multibody systems
70J10 Modal analysis in linear vibration theory
70-08 Computational methods for problems pertaining to mechanics of particles and systems

Keywords:

modal analysis; eigenfrequency; augmented eigenvector; orthogonality
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Full Text: DOI

References:

[1] Schiehlen, W.: Multibody system dynamics: roots and perspectives. Multibody Syst. Dyn. 1, 149–188 (1997) · Zbl 0901.70009 · doi:10.1023/A:1009745432698
[2] Shabana, A.A.: Flexible multibody dynamics: review of past and recent developments. Multibody Syst. Dyn. 1, 189–222 (1997) · Zbl 0893.70008 · doi:10.1023/A:1009773505418
[3] Holzer, H.: Die Berechnung der Drehsenwingungen. Springer, Berlin (1921) · JFM 48.0884.12
[4] Myklestad, N.O.: New method of calculating natural modals of coupled bending-torsion vibration of beams. Trans. ASME 67, 61–67 (1945)
[5] Thomson, W.T.: Matrix solution of vibration of nonuniform beams. J. Appl. Mech. 17, 337–339 (1950) · Zbl 0040.40104
[6] Pestel, E.C., Leckie, F.A.: Matrix Method in Elastomechanics. McGraw-Hill, New York (1963)
[7] Rubin, S.: Transmission matrices for vibrators and their relation to admittance and impedance. J. Eng. Mater. Technol. 86, 9–21 (1964)
[8] Rubin, S.: Review of mechanical immittance and transmission matrix concepts. J. Acoust. Soc. Am. 41, 1171–1179 (1967) · doi:10.1121/1.1910455
[9] Targoff, W.P.: The associated matrices of bending and coupled bending-torsion vibrations. J. Aeronaut. Sci. 14, 579–582 (1947)
[10] Lin, Y.K.: Probabilistic Theory of Structure Dynamics. McGraw-Hill, New York (1967)
[11] Mercer, C.A., Seavey, C.: Prediction of natural frequencies and norma1 modals of skin-stringer panel rows. J. Sound Vib. 6, 149–162 (1967) · doi:10.1016/0022-460X(67)90167-8
[12] Lin, Y.K., McDaniel, T.J.: Dynamics of beam-type periodic structures. J. Eng. Mater. Technol. 91, 1133–1141 (1969)
[13] Mead, D.J., Gupta, G.S.: In: Propagation of flexural waves in infinite, damped rib-skin structures. United States Air Force Report, AFML-TR-70-13 (1970)
[14] Mead, D.J.: Vibration response and wave propagation in periodic structures. J. Eng. Mater. Technol. 93, 783–792 (1971)
[15] Henderson, J.P., McDaniel, T.J.: The analysis of curved multi-span structures. J. Sound Vib. 18, 203–219 (1971) · doi:10.1016/0022-460X(71)90345-2
[16] McDaniel, T.J.: Dynamics of circular periodic structures. J. Aircr. 8, 143–149 (1971) · doi:10.2514/3.44245
[17] McDaniel, T.J., Logan, J.D.: Dynamics of cylindrical she1ls with variable curvature. J. Sound Vib. 19, 39–48 (1971) · Zbl 0221.73028 · doi:10.1016/0022-460X(71)90421-4
[18] Murthy, V.R., Nigam, N.C.: Dynamics characteristics of stiffened rings by transfer matrix approach. J. Sound Vib. 39, 237–245 (1975) · Zbl 0298.73097 · doi:10.1016/S0022-460X(75)80222-7
[19] Murthy, V.R., McDaniel, T.J.: Solution bounds to structural systems. AIAA J. 14, 111–113 (1976) · Zbl 0352.73041 · doi:10.2514/3.7063
[20] McDaniel, T.J., Murthy, V.R.: Solution bounds for varying geometry beams. J. Sound Vib. 44, 431–448 (1976) · Zbl 0328.73041 · doi:10.1016/0022-460X(76)90513-7
[21] Dokanish, M.A.: A new approach for plate vibration: combination of transfer matrix and finite element technique. J. Mech. Des. 94, 526–530 (1972)
[22] Ohga, M., Shigematus, T.: Transient analysis of plates by a combined finite element transfer matrix method. Comput. Struct. 26, 543–549 (1987) · Zbl 0612.73079 · doi:10.1016/0045-7949(87)90002-2
[23] Xue, H.: A combined dynamic finite element riccati transfer matrix method for solving non-linear eigenproblems of vibrations. Comput. Struct. 53, 1257–1261 (1994) · Zbl 0894.73181 · doi:10.1016/0045-7949(94)90393-X
[24] Loewy, R.G., Degen, E.E., Shephard, M.S.: Combined finite element-transfer matrix method based on a mixed formulation. Comput. Struct. 20, 173–180 (1985) · Zbl 0574.73087 · doi:10.1016/0045-7949(85)90066-5
[25] Loewy, R.G., Bhntani, N.: Combined finite element-transfer matrix method. J. Sound Vib. 226(5), 1048–1052 (1999) · doi:10.1006/jsvi.1999.2332
[26] Horner, G.C., Pilkey, W.D.: The riccati transfer matrix method. J. Mech. Des. 1, 297–302 (1978) · doi:10.1115/1.3453915
[27] Rui, X.T., Lu, Y.Q.: Transfer matrix method of vibration of multibody system. Chin. J. Astronaut. 16(3), 41–47 (1995)
[28] Rui, X.T., Sui, W.H., Shao, Y.Z.: Transfer matrix of rigid body and its application in multibody dynamics. Chin. J. Astronaut. 14(4), 82–87 (1993)
[29] Lu, Y.Q., Rui, X.T.: Eigenvalue problem, orthogonal property and response of multibody system. In: Zhang, J.H., Zhang, X.N. (eds.) ICAPV 2000, Proceedings of International Conference on Advanced Problems in Vibration Theory and Applications. Science Press, Beijing (2000)
[30] Kumar, A.S., Sankar, T.S.: A new transfer matrix method for response analysis of large dynamic systems. Comput. Struct. 23, 545–552 (1986) · Zbl 0583.73079 · doi:10.1016/0045-7949(86)90097-0
[31] Rui, X.T., Lu, Y.Q., Ling, P. et al.: Discrete time transfer matrix method for mutibody system dynamics. In: Euromech Colloquium 404 on Advances in Computational Multibody Dynamics, Lisbon, Portugal, 1999, pp. 93–108 (1999)
[32] Rui, X.T., He, B., Lu, Y.Q., et al.: Discrete time transfer matrix method for multibody system dynamics. Multibody Syst. Dyn. 14(3–4), 317–344 (2005) · Zbl 1146.70323 · doi:10.1007/s11044-005-5006-1
[33] Kane, T.R., Likine, P.W., Levinson, D.A.: Spacecraft Dynamics. McGraw-Hill, New York (1983)
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