Abstract:
Active isolation of a vibrating rigid mass from a flexible simply supported beam is investigated theoretically and experimentally. Results obtained using vibrational power transmission as a cost function are compared with those obtained using base acceleration and transmitted force as cost functions. One problem with using vibratory power transmission as a cost function is the lack of correlation between the reference and error signals due to the frequency doubling effect of the multiplication operation used to obtain power. This problem is addressed by heterodyning the frequency doubled-error signal with the reference signal to obtain an error signal with the same frequency components as the reference signal, but with the amplitude dependent on the frequency doubled-error signal amplitude. Theoretical results indicate that it is possible to achieve zero vibratory power transmission into the beam irrespective of whether the cost function used is vibratory power, beam acceleration at the base of the isolator, or transmitted force. Experimental results show that similar isolation efficiencies are obtained for all three types of cost function with the achievable efficiency dependent upon the accuracy of the digital control system.