Modal characteristics of a flexible beam with multiple distributed actuators

A flexible structure with surface-bonded piezoceramic patches is modelled using Timoshenko beam theory. Exact mode shapes and natural frequencies associated with the flexural motion are computed for various piezoceramic distributed actuator arrangements. The effects of patch placement and of shear on the modal characteristics are demonstrated using a cantilevered beam as an example. Perfect bonding of the piezoceramic to the beam substructure is assumed, and for the purposes of this paper only passive piezoceramic properties are considered. The modelling technique and results obtained in a closed form are intended to assist investigations into the modelling and control of active structures with surface-bonded piezoceramic actuators.