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RESEARCH PAPERS: Vibration and Sound

Application of Transfer Matrix Method to Analysis of Transient Response of Beam

[+] Author and Article Information
Moriaki Goya

University of The Ryukyus, Nishihara, Okinawa 903-1, Japan

Takuo Hayashi

Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560, Japan

Koichi Ito

Tohoku University, Aramaki, Sendai, Miyagi 980, Japan

Hiroshi Ohki

Mechanical Engineering Research Laboratory, Hitachi Ltd., 502 Kandatsu, Tsuchiura, Ibaraki 300, Japan

J. Vib., Acoust., Stress, and Reliab 109(3), 248-254 (Jul 01, 1987) (7 pages) doi:10.1115/1.3269428 History: Received February 25, 1987; Online November 23, 2009

Abstract

The transient responses of an elastic beam to large dynamic deformations were analyzed numerically, using the transfer matrix method. Geometrically nonlinear differential equations were linearized by introducing increments of unknown functions, and the resulting linear equations were approximated by finite difference equations. A field transfer matrix was introduced for the analyses of large deformations; this determined the relationship between the incremental state vectors at both ends of the elastic segments. The Newmark β formulation was chosen to approximate the equation of motion for concentrated masses. A concentrated mass point transfer matrix and an inhomogeneous vector were introduced for analyses of the transient responses of the beams. A superposition scheme for the transfer matrix method was proposed as an effective means of obtaining a solution satisfying the boundary conditions at both ends of the beam.

Copyright © 1987 by ASME
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