Optimal excitation of a rectangular plate resting on an elastic foundation by a piezoelectric actuator

In this paper, a simply supported rectangular plate subject to in-plane forces, resting on an elastic foundation and excited by a PZT actuator, is studied. A closed-form solution has been obtained to describe the plate vibration. Based on this solution, the optimal placement of the PZT actuator in terms of maximizing the plate deflection is calculated and discussed. It is observed that the pattern of the optimal locations of the PZT actuator can be represented by a simple function, namely, the combined position mode function (CPMF). A simple yet general procedure to determine the optimal excitation locations is thus proposed based on the above observation. This procedure only requires the calculation of natural frequencies of the plate and the CPMF, thus alleviating the computational effort in searching for the optimal PZT locations.