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Research Papers

An Augmented State Formulation for Modeling and Analysis of Multibody Distributed Dynamic Systems

[+] Author and Article Information
K. Noh

Chief Research Engineer
LG PRI,
222 LG-ro Jinwin-myeon,
Pyeongtaek-si, Gyeonggi-do 451-713, Korea
e-mail: k.noh@lge.com

B. Yang

Professor
Fellow ASME
Department of Aerospace and
Mechanical Engineering,
University of Southern California,
3650 McClintock Avenue, Room 430,
Los Angeles, CA 90089-1453
e-mail: bingen@usc.edu

1Corresponding author.

Manuscript received May 8, 2013; final manuscript received November 26, 2013; accepted manuscript posted November 29, 2013; published online January 7, 2014. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 81(5), 051011 (Jan 07, 2014) (9 pages) Paper No: JAM-13-1187; doi: 10.1115/1.4026124 History: Received May 08, 2013; Revised November 26, 2013; Accepted November 29, 2013

Multibody distributed dynamic systems are seen in many engineering applications. Developed in this investigation is a new analytical method for a class of branched multibody distributed systems, which is called the augmented distributed transfer function (DTFM). This method adopts an augmented state formulation to describe the interactions among multiple distributed and lumped bodies, which resolves the problems with conventional transfer function methods in modeling and analysis of multibody distributed systems. As can be seen, the augmented DTFM, without the need for orthogonal system eigenfunctions, produces exact and closed-form solutions of various dynamic problems, in both frequency and time domains.

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References

Prestel, E. C., and Leckie, F. A., 1963, Matrix Methods in Elastomechanics, McGraw-Hill, New York.
Dowell, E. H., 1972, “Free Vibration of an Arbitrary Structure in Terms of Component Modes,” ASME J. Appl. Mech., 39, pp. 727–732. [CrossRef]
Hallquist, J., and Snyder, V. W., 1973, “Linear Damped Vibratory Structures With Arbitrary Support Conditions,” ASME J. Appl. Mech., 40, pp. 312–313. [CrossRef]
Mead, D. J., 1971, “Vibration Response and Wave Propagation in Periodic Structures,” ASME J. Eng. Ind., 93(3), pp. 783–792. [CrossRef]
Mead, D. J., and Yaman, Y., 1990, “The Harmonic Response of Uniform Beams on Multiple Linear Supports: A Flexural Wave Analysis,” J. Sound Vib., 141, pp. 465–484. [CrossRef]
Bergman, L. A., and Nicholson, J. W., 1985, “Forced Vibration of a Damped Combined Linear System,” ASME J. Vib. Acoust. Stress Reliability, 107(3), pp. 275–281. [CrossRef]
Doyle, J. F., 1997, Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, 2nd ed., Springer, New York.
Lee, U., 2009, Spectral Element Method in Structural Dynamics, John Wiley and Sons, Singapore.
Kelly, S. G., and Srinivas, S., 2009, “Free Vibrations of Elastically Connected Stretched Beams,” J. Sound Vib., 326, pp. 883–893. [CrossRef]
Butkoviskiy, A. G., 1983, Structural Theory of Distributed Systems, Halsted, John Wiley and Sons, New York.
Yang, B., and Tan, C. A., 1992, “Transfer Functions of One-Dimensional Distributed Parameter Systems,” ASME J. Appl. Mech., 59, pp. 1009–1014. [CrossRef]
Yang, B., 1994, “Distributed Transfer Function Analysis of Complex Distributed Parameter Systems,” ASME J. Appl. Mech., 61, pp. 84–92. [CrossRef]
Yang, B., 2005, Stress, Strain, and Structural Dynamics: An Interactive Handbook of Formulas, Solutions, and MATLAB Toolboxes, Elsevier Science, Boston.
Yang, B., 2010, “Exact Transient Vibration of Stepped Bars, Shafts and Strings Carrying Lumped Masses,” J. Sound Vib., 329, pp. 1191–1207. [CrossRef]
Yang, B., and Noh, K., 2012, “Exact Transient Vibration of Non-Uniform Bars, Shafts and Strings Governed by Wave Equations”, Int. J. Struct. Stability Dyn., 12(4), p. 1250022. [CrossRef]
Yang, B., and Mote, C.D., Jr., 1991, “Frequency–Domain Vibration Control of Distributed Gyroscopic Systems,” ASME J. Dyn. Syst. Measure. Control, 113(1), pp. 18–25. [CrossRef]

Figures

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Fig. 1

Schematic of a branched multibody distributed system [12]

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Fig. 2

Distributed subsystems serially connected

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Fig. 3

Pointwise connection of two distributed subsystems

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Fig. 4

Distributed connection of two distributed systems

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Fig. 5

A coupled beam structure

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Fig. 6

The characteristic functions of the coupled beam structure: (a) detK(Jω) in Ref. [12]; and (b) Δ(ω) in Eq. (40)

Grahic Jump Location
Fig. 8

The first four mode shapes of the frame structure: (a) mode 1: ω1 = 83.524, (b) mode 2: ω2 = 113.05, (c) mode 3: ω3 = 206.44, and (d) mode 4: ω4 = 271.71

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