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Discrete time transfer matrix method for multibody system dynamics. (English) Zbl 1146.70323

Summary: A new method for multibody system dynamics is proposed in this paper. This method, named as discrete time transfer matrix method of multibody system (MS-DT-TMM), combines and expands the advantages of the transfer matrix method (TMM), transfer matrix method of vibration of multibody system (MS-TMM), discrete time transfer matrix method (DT-TMM) and the numerical integration procedure. It does not need the global dynamics equations for the study of multibody system dynamics. It has the modeling flexibility and a small size of matrices, and can be applied to a wide range of problems including multi-rigid-body system dynamics and multi-flexible-body system dynamics. This method is simple, straightforward, practical, and provides a powerful tool for the study of multibody system dynamics. Formulations of the method as well as some numerical examples of multi-rigid-body system dynamics and multi-flexible-body system dynamics to validate the method are given.

MSC:

70E55 Dynamics of multibody systems
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[1] Schiehlen, W., ’Multibody system dynamics: Roots and perspectives’, Multibody System Dynamics 1, 1997, 149–188. · Zbl 0901.70009
[2] Shabana, A.A., ’Flexible multibody dynamics: Review of past and recent developments’, Multibody System Dynamics 1, 1997, 189–222. · Zbl 0893.70008
[3] Holzer, H., Die Berechnung der Drehsenwingungen, Springer, Berlin, 1921. · JFM 48.0884.12
[4] Myklestad, N.O., ’New method of calculating natural modes of coupled bending-torsion vibration of beams’, Transaction of The ASME 67, 1945, 61–67.
[5] Thomson, W.T., ’Matrix solution of vibration of nonuniform beams’, Journal of Applied Mechanics 17, 1950, 337–339. · Zbl 0040.40104
[6] Pestel, E.C. and Leckie, F.A., Matrix Method in Elastomechanics, McGraw-Hil1, New York, 1963.
[7] Rubin, S., ’Transmission matrices for vibrators and their relation to admittance and impedance’, Journal of Engineering Materials and Technology 86, 1964, 9–21.
[8] Rubin, S., ’Review of mechanical immittance and transmission matrix concepts’, Journal of the Acoustical Society of America 41, 1967, 1171–1179.
[9] Targoff, W.P., The associated matrices of bending and coupled bending-torsion vibrations, Journal of Aeronautics Science 14, 1947, 579–582.
[10] Lin, Y.K., Probabilistic Theory of Structure Dynamics, McGraw-Hill, New York, l967.
[11] Mercer, C.A. and Seavey, C., ’Prediction of natural frequencies and norma1 modes of skin-stringer panel rows’, Journal of Sound and Vibration 6, 1967, 149–162.
[12] Lin, Y.K. and McDaniel, T.J., ’Dynamics of beam-type periodic structures’, Journal of Engineering Materials and Technology 91, 1969, 1133–1141.
[13] Mead, D.J. and Gupta, G.S., Propagation of Flexural Waves in Infinite, Damped Rib-Skin Structures, United States Air Force Report, AFML-TR-70-l3, l970.
[14] Mead, D.J., ’Vibration response and wave propagation in periodic structures’, Journal of Engineering Materials and Technology 93, 1971, 783–792.
[15] Henderson, J.P. and McDaniel, T.J., ’The analysis of curved multi-span structures’, Journal of Sound and Vibration l8, 1971, 203–219.
[16] McDaniel, T.J., ’Dynamics of circular periodic structures’, Journal of Aircraft 8, 1971, l43–149.
[17] McDaniel, T.J. and Logan, J.D., ’Dynamics of cylindrical she1ls with variable curvature’, Journal of Sound and Vibration 19, 1971, 39–48. · Zbl 0221.73028
[18] Murthy, V.R. and Nigam, N.C., ’Dynamics characteristics of stiffened rings by transfer matrix approach’, Journal of Sound and Vibration 39, 1975, 237–245. · Zbl 0298.73097
[19] Murthy, V.R. and McDaniel, T.J., ’Solution bounds to structural systems’, AIAA Journal 14, 1976, 111–113. · Zbl 0352.73041
[20] McDaniel, T.J. and Murthy, V.R., ’Solution bounds for varying geometry beams’, Journal of Sound and Vibration 44, 1976, 431–448. · Zbl 0328.73041
[21] Dokanish, M.A., ’A new approach for plate vibration: Combination of transfer matrix and finite element technique’, Journal of Mechanical Design 94, 1972, 526–530.
[22] Ohga, M. and Shigematus, T., ’Transient analysis of plates by a combined finite element transfer matrix method’, Computers & Structures 26, 1987, 543–549. · Zbl 0612.73079
[23] Xue, H., ’A combined dynamic finite element riccati transfer matrix method for solving non-linear eigenproblems of vibrations’, Computers & Structures 53, 1994, 1257–1261. · Zbl 0894.73181
[24] Loewy, R.G., Degen, E.E. and Shephard, M.S., ’Combined finite element-transfer matrix method based on a mixed formulation’, Computers & Structures 20, 1985, 173–180. · Zbl 0574.73087
[25] Loewy, R.G. and Bhntani, N., ’Combined finite element-transfer matrix method’, Journal of Sound and Vibration 226(5), 1999, 1048–1052.
[26] Horner, G.C. and Pilkey, W.D., ’The riccati transfer matrix method’, Journal of Mechanical Design 1, 1978, 297–302.
[27] Rui, X.T. and Lu, Y.Q., ’Transfer matrix method of vibration of multibody system’, Chinese Journal of Astronautics 16(3), 1995, 41–47.
[28] Rui, X.T., Sui, W.H. and Shao, Y.Z., ’Transfer matrix of rigid body and its application in multibody dynamics’, Chinese Journal of Astronautics 14(4), 1993, 82–87.
[29] Lu, Y.Q. and Rui, X.T., ’Eigenvalue problem, orthogonal property and response of multibody system’, in J.H. Zhang and X.N. Zhang (eds.), ICAPV 2000, Proceedings of International Conference on Advanced Problems in Vibration Theory and Applications, Science Press, Beijing, 2000.
[30] Kumar, A.S. and Sankar, T.S., ’A new transfer matrix method for response analysis of large dynamic systems’, Computers & Structures 23, 1986, 545–552. · Zbl 0583.73079
[31] Kane, T.R., Likine, P.W. and Levinson, D.A., Spacecraft Dynamics, McGraw-Hill, New York, 1983.
[32] Dokainish, M.A. and Subbaraj, K., ’A study of direct time-integration methods in computational structural dynamics-I. Explicit methods’, Computers & Structures 32(6), 1989, 1371–1386. · Zbl 0702.73072
[33] Subbaraj, K. and Dokainish, M.A., ’A study of direct time-integration methods in computational structural dynamics-II. Implicit methods’, Computers & Structures 32(6), 1989, 1387–1401. · Zbl 0702.73073
[34] Kübler, R. and Schiehlen, W., ’Two methods of simulator coupling’, Mathematical and Computer Modelling of Dynamical Systems 6, 2000, 93–113. · Zbl 0962.65107
[35] Banerjee, A.K. and Nagarajan, S., ’Efficient simulation of large overall motion of Beams undergoing large deflection’, Multibody System Dynamics 1, 1997, 113–126. · Zbl 0889.73077
[36] Wang, Y. and Huston, R.L., ’A lumped parameter method in the nonlinear analysis of flexible multibody system’, Computers & Structures 50(3), 1994, 421–432. · Zbl 0804.73078
[37] Valasek, M., On the Efficient Implementation of Multibody System Formulations, Technical Report institutsbericht, IB-17, University Stuttgart, 1990.
[38] Li, Y., ’Modified algorithm of transfer matrix method of eigenvalue problem’, Chinese Journal of Aerospace Power 6(3), 1991, 249–250.
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