State Space Modeling of an Acoustic Duct With an End-Mounted Speaker

[+] Author and Article Information
R. Venugopal, D. S. Bernstein

Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2118

J. Vib. Acoust 120(3), 770-775 (Jul 01, 1998) (6 pages) doi:10.1115/1.2893896 History: Received March 01, 1996; Revised March 01, 1997; Online February 26, 2008


This paper develops a state space model of the dynamics of an acoustic duct with end-mounted speakers. The initial model formulation includes the forcing term as part of the boundary conditions. The shifted particle velocity is then defined to transform the nonhomogeneous boundary conditions into homogeneous boundary conditions and thus develop the state space model. It is shown that the speaker and acoustic dynamics interact by means of feedback in which the speaker creates an acoustic field, which, in turn, affects the motion of the speaker cone. This interaction is studied using positive real closed-loop feedback analysis, and shifts in the modal frequencies of the duct due to the presence of the end-mounted speaker are predicted.

Copyright © 1998 by The American Society of Mechanical Engineers
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