Journal of Theoretical
and Applied Mechanics

50, 3, pp. 769-784, Warsaw 2012

Optimal vibration control of conical shells with collocated helical sensor/actuator pairs

H. Li, S.D. Hu, H.S. Tzou, Z.B. Chen
This paper focuses on the optimal vibration control of clamped-free conical shells using
distributed helical piezoelectric sensor/actuator (S/A) pairs. Based on the independent modal space
control, the response of conical shell to external excitations is represented by the summation of all participating natural modes and their respective modal participation factors, and each mode can be controlled independently. The modal equation is transformed into the linear state space form. The
linear quadratic (LQ) controllers are designed for each independent mode. The optimal gain matrix
is related to the ratio $ G^*$ between the control voltage and sensing signal by the modal control force per unit voltage $ B_2$ and the sensing signal per unit displacement $ C_1$. Because $ B_2$ and $ C_1$ change with locations of the S/A pair, the optimal control effects, modal control forces and corresponding optimal control voltages are evaluated using two S/A pairs at different locations. The results indicate that the optimal control method is effective in vibration control of the shell. The optimal control effect also depends on the location of the S/A pair and modal shapes as well as the modal control force and input voltage.
Keywords: smart structure; conical shell; diagonal sensor/actuator; optimal vibration control