One-dimensional acoustic response of ducts is a classical engineering problem. The acoustic response in a hard-walled duct with a dissipative end condition can be visualized as a combination of standing and propagating wave response. A modal decomposition based on the system eigenvalues derived here produces an infinite order state space model incorporating this behavior. This allows computation of system transient response as well as frequency response. The shapes of duct characteristic response derived here are in stark contrast to those previously available for ducts. It is shown that the traditionally employed sinusoidal responses cannot be used to compute duct response for dissipative ends. A comparison between the frequency response of a finite order truncation of the new state space model and a previous exact frequency response is included. The new transient response of the truncated state space model is demonstrated and truncation error investigated. High frequency behavior of the state space model is discussed.
State Space Representation of the Nonself-Adjoint Acoustic Duct System
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Hull, A. J., Radcliffe, C. J., Miklavcˇicˇ, M., and MacCluer, C. R. (October 1, 1990). "State Space Representation of the Nonself-Adjoint Acoustic Duct System." ASME. J. Vib. Acoust. October 1990; 112(4): 483–488. https://doi.org/10.1115/1.2930132
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