Modal decomposition results for active control of energy density

Abstract

In recent years, an alternative sensing approach has been developed for active control, based on minimizing the acoustic energy density at the error sensor location(s). This new approach has been tested both numerically and experimentally, with the results indicating that one can often achieve improved global attenuation of the field by minimizing the acoustic energy density, rather than the sum of the squared pressures. Previous results from minimizing the energy density at the error sensors have concentrated on investigating the control that can be achieved by looking at the global energy in the field before and after control, and also by looking at the attenuation that can be achieved as a function of frequency. However, it has also been found that additional insight can be gained by examining the acoustic field in terms of the acoustic modes contributing to the acoustic field. This paper will present some of the modal decomposition results obtained for different active control approaches. These results provide insight into the control mechanisms and provide indications as to why one can often achieve improved global attenuation by minimizing the acoustic energy density rather than the squared pressure.

Active control of energy density in a one-dimensional waveguide: A cautionary note (L)

“…[10][11][12][13][14][15][16][17][18][19] Acoustic energy density, defined as the sum of the acoustic potential and kinetic energy densities at a point, is commonly estimated using the two-microphone method 1 and is given by ͑see the Appendix͒…”