Research Papers

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

[+] Author and Article Information
K. Noh

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

B. Yang

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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Grahic Jump Location
Fig. 1

Schematic of a branched multibody distributed system [12]

Grahic Jump Location
Fig. 2

Distributed subsystems serially connected

Grahic Jump Location
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

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

Grahic Jump Location
Fig. 6

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




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