Given the benefits of using acoustic energy density for active noise control in enclosures, it was hypothesized that active structural acoustic control (ASAC) might also benefit by incorporating an energy-based structural error quantity. Power flow, or structural intensity, and structural energy density were studied for use in an ASAC system. Power flow was found to be unsuitable for general-purpose use in this application. Its minimization properties are such that for a general case, it may be impossible to predict structural or acoustic response based on a minimization of power flow amplitude in a two-dimensional setting. Additionally, sensor placement is complicated by the large changes in power flow field orientation caused by a small mass loading for a lightweight structure. Structural energy density was found to be a suitable error metric, and provides a slight improvement over velocity-based ASAC in enclosed spaces. A genetic algorithm was used to study structural energy density sensor placement on a simply supported plate. At modal frequencies, optimum control was achieved by placing the sensor at antinodes. The placement of the control force was found to be less critical, but showed a slight tendency towards locations remote from the disturbance force with low velocity cross-derivative.
Structural energy density and structural power flow have long been used as metrics in the active control of vibrating structures. The greater portion of this previous work has focused on frequency-domain methods which incorporate assumptions about the relative contributions of near-field and far-field energy components. This paper describes the implementation of filtered-x-based time-domain control schemes which utilize 9- and 13-accelerometer arrays to estimate and control structural energy density and structural power flow, respectively. Experiments were performed on a clamped steel plate excited and controlled by various combinations of loudspeakers and electrodynamic shakers in a frequency range from 25 to 100 Hz. Analog circuitry was used to estimate spatial derivatives and reduce channel count. The development of control laws incorporating the effects of the analog circuitry is presented. Control attentuation results are given, sensor placement is discussed, and implementation challenges are addressed. [This work is supported by NSF Grant 0826554.]
Power flow in structures has been a topic of research for the past few decades. Many different methods for determining structural power flow magnitude and direction have been developed and proven. Structural energy density methods have likewise been developed. In this paper, a study of both structural energy density and power flow in a plate and their influence on the acoustic field is presented. Structural energy density and power flow were determined using equations typically used with accelerometer arrays but adapted for use with a scanning laser doppler vibrometer. Experiments were performed from 25 to 100 Hz by exciting the plate at single frequencies but using different excitation points and methods at each frequency. In some cases two sources of excitation were used to alter the power flow response, giving a broader basis for concluding relationships. Both speaker and shakers were used as sources. The acoustic intensity in the room was calculated at approximately 3 in. from the vibrating plate. Relationships between structural energy density, power flow, and the acoustic field variables are presented.
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