A Transfer-Function Formulation For Nonuniformly Distributed Parameter Systems

[+] Author and Article Information
B. Yang, H. Fang

Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453

J. Vib. Acoust 116(4), 426-432 (Oct 01, 1994) (7 pages) doi:10.1115/1.2930445 History: Received December 01, 1992; Revised June 01, 1993; Online June 17, 2008


This paper studies a transfer-function formulation for general one-dimensional, nonuniformly distributed systems, subject to arbitrary boundary conditions and external disturbances. In the development, the governing equations of the nonuniform system are cast into a state-space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state-space equation. Two approximate methods, the step-function approximation and truncated Taylor series, are proposed to evaluate the fundamental matrix. With the transfer-function formulation, various dynamics and control problems for the nonuniformly distributed system can be conveniently addressed. The transfer-function analysis also is applied to constrained/combined nonuniformly distibuted systems. The method developed is illustrated on two nonuniform beams.

Copyright © 1994 by The American Society of Mechanical Engineers
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