Transfer matrix method for linear multibody system

Abstract A new method for linear hybrid multibody system dynamics is proposed in this paper. This method, named as transfer matrix method of linear multibody system (MSTMM), expands the advantages of the traditional transfer matrix method (TMM). The concepts of augmented eigenvector and equation of motion of linear hybrid multibody system are presented at first to find the orthogonality and to analyze the responses of the hybrid multibody system using modal method. If using this method, the global dynamics equation is not needed in the study of linear hybrid multibody system dynamics. The MSTMM has a small size of matrix and higher computational speed, and can be applied to linear multi-rigid-body system dynamics, linear multi-flexible-body system dynamics and linear hybrid multibody system dynamics. This method is simple, straightforward, practical, and provides a powerful tool for the study on linear hybrid multibody system dynamics. This method can be used in the following: (1) Solve the eigenvalue problem of linear hybrid multibody systems. (2) Obtain the orthogonality of eigenvectors of linear hybrid multibody systems. (3) Realize the accurate analysis of the dynamics response of linear hybrid multibody systems. (4) Find the connected parameters between bodies used in the computation of linear hybrid multibody systems. A practical engineering system is taken as an example of linear multi-rigid-flexible-body system, the dynamics model, the transfer equations and transfer matrices of various bodies and hinges; the overall transfer equation and overall transfer matrix of the system are developed. Numerical example shows that the results of the vibration characteristics and the response of the hybrid multibody system received by MSTMM and by experiment have good agreements. These validate the proposed method.

[1]  M. Ohga,et al.  Transient analysis of plates by a combined finite element-transfer matrix method , 1987 .

[2]  S. Rubin.  Transmission Matrices for Vibration and Their Relation to Admittance and Impedance , 1964 .

[3]  Y. K. Lin,et al.  Dynamics of Beam-Type Periodic Structures , 1969 .

[4]  Walter P. Targoff.  The Associated Matrices of Bending and Coupled Bending-Torsion Vibrations , 1947 .

[5]  T. J. McDaniel.  Dynamics of Circular Periodic Structures , 1971 .

[6]  C. A. Mercer,et al.  PREDICTION OF NATURAL FREQUENCIES AND NORMAL MODES OF SKIN-STRINGER PANEL ROWS. , 1967 .

[7]  V. R. Murthy,et al.  Solution bounds for varying geometry beams , 1976 .

[8]  Garnett C. Horner,et al.  The Riccati Transfer Matrix Method , 1978 .

[9]  T. S. Sankar,et al.  A new transfer matrix method for response analysis of large dynamic systems , 1986 .

[10]  M. A. Dokainish,et al.  A New Approach for Plate Vibrations: Combination of Transfer Matrix and Finite-Element Technique , 1972 .

[11]  V. R. Murthy,et al.  Solution bounds to structural systems , 1976 .

[12]  Ahmed A. Shabana,et al.  Flexible Multibody Dynamics: Review of Past and Recent Developments , 1997 .

[13]  V. R. Murthy,et al.  Dynamic characteristics of stiffened rings by transfer matrix approach , 1975 .

[14]  T. J. McDaniel,et al.  Dynamics of cylindrical shells with variable curvature , 1971 .

[15]  D. J. Mead.  Vibration Response and Wave Propagation in Periodic Structures , 1971 .

[16]  Werner Schiehlen,et al.  Multibody System Dynamics: Roots and Perspectives , 1997 .

[17]  Xue Huiyn,et al.  A combined dynamic finite element—Riccati transfer matrix method for solving non-linear eigenproblems of vibrations , 1994 .

[18]  S. Rubin.  Review of Mechanical Immittance and Transmission Matrix Concepts , 1966 .

[19]  Guoping Wang,et al.  Discrete Time Transfer Matrix Method for Multibody System Dynamics , 2005 .

[20]  D. J. Mead,et al.  PROPAGATION OF FLEXURAL WAVES IN INFINITE, DAMPED RIB-SKIN STRUCTURES. , 1970 .

[21]  N. Bhutani,et al.  COMBINED FINITE ELEMENT-TRANSFER MATRIX METHOD , 1999 .

[22]  Mark S. Shephard,et al.  Combined finite element-transfer matrix method based on a mixed formulation , 1985 .

[23]  Sheldon Rubin.  Mechanical Immittance‐ and Transmission‐Matrix Concepts , 1967 .

[24]  T. J. McDaniel,et al.  The analysis of curved multi-span structures , 1971 .