Active power minimisation and power absorption in a plate with force and moment excitation

This paper presents a comparison of the active control strategies of minimizing the total power supplied to a plate and maximizing the power absorbed by the secondary source. Force and moment excitations of infinite and finite plates are considered. For an infinite plate analytic solutions can be obtained for the total power supplied to the plate by the primary and secondary actuator arrays when using the two control strategies. Minimizing the power supplied by a primary force or moment with a secondary force or moment can produce large attenuation provided that the two sources are close together compared with a flexural wavelength. Minimizing the power supplied by a primary force with a secondary moment can also give attenuation of up to 5 dB when the spacing between the sources is about 0·3 times the flexural wavelength. In contrast to the acoustic case, for the infinite plate the total power supplied is generally reduced when the power absorbed by the secondary source is maximized. On a finite panel, however, maximizing the power absorbed by the secondary source can significantly increase the total power supplied. The strategy of minimizing the total power supplied can give considerably larger values of attenuation for finite rather than infinite plates, particularly at higher frequencies. This is because the structural modes can be actively controlled. A particularly efficient secondary actuator for total power minimisation appears to be an independently adjustable, but collocated, force and moment pair.