Quasi-static and dynamic electromechanical response of piezoelectric multilayer cantilever beams

Piezoelectric multilayer cantilever beams were considered with the aim to establish a simple but general theoretical model, fabricate such beams by a procedure suitable for devices on millimetre scale such as actuators, and study their quasi-static and dynamic electromechanical responses. In addition to Euler–Bernoulli assumptions, the beams were assumed to be lossless and have linear piezoelectric response. Four types of beams of nominal length 10 mm, width 2 mm and thickness either 55 or 86 μm, and with two asymmetric configurations of 14 or 15 layers, were fabricated. From top to bottom, each beam consisted of six aluminium electrode layers alternating with five active P(VDF-TrFE) layers, of one passive such layer, and of one polyimide and one copper layer, or vice versa. The thicknesses of the layers and of the beam were determined by use of focused ion beam, scanning electron microscope, light microscope, and Heidenhain probe. Both theoretical and experimental results for resonance frequencies and transverse tip displacement per unit driving voltage showed fair overall agreement from quasi-static conditions to frequencies above the second resonance frequency. Deviations observed are mainly due to variations resulting from the manufacturing process, to nonlinear piezoelectricity and to the presence of losses.