American Institute of Mathematical Sciences

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January  1995, 1(1): 119-149. doi: 10.3934/dcds.1995.1.119

Feedback control of noise in a 2-D nonlinear structural acoustics model

H. T. Banks 1, and  R.C. Smith 2,

1. 

Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212, United States
2. 

ICASE, NASA Langley Research Center, Hampton, VA 23681, United States

Received  October 1994 Published  October 1994

A time domain feedback control methodology for reducing sound pressure levels in a nonlinear 2-D structural acoustics application is presented. The interior noise in this problem is generated through vibrations of one wall of the cavity (in this case a beam), and control is implemented through the excitation of piezoceramic patches which are bonded to the beam. These patches are mounted in pairs and are wired so as to create pure bending moments which directly affect the manner in which the structure vibrates. Th application of control in this manner leads to an unbounded control input term and the implications of this are discussed. The coupling between the beam vibrations and the interior acoustic response is inherently nonlinear, and this is addressed when developing a control scheme for the problem. Gains for the problem are calculated using a periodic LQR theory and are then fed back into the nonlinear system with results being demonstrated by a set of numerical examples. In particular, these examples demonstrate the viability of the method in cases involving excitation involving a large number of frequencies through both spatially uniform and nonuniform exterior forces.
Keywords: Feedback control, acoustics model, LQR theory..
Mathematics Subject Classification: 34H05, 60H4.
Citation: H. T. Banks, R.C. Smith. Feedback control of noise in a 2-D nonlinear structural acoustics model. Discrete and Continuous Dynamical Systems, 1995, 1 (1) : 119-149. doi: 10.3934/dcds.1995.1.119
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