Composite modeling of flexible structures with bonded piezoelectric film actuators and sensors

In this paper, the interaction equations for a flexible beam with multiple-bonded piezoelectric films are derived. Any flexible structure composed of flexible beam members can be analyzed with these equations. The interaction equations account for the effects of shaped piezoelectric films, that is, the film's electrodes may be etched with geometrical shapes and the poling direction may be altered by splicing. The derivation is based on a generalization of the interaction equations for a single film. The interaction equations make use of the vibrational modes of a structure. The vibrational modes can be derived either analytically or numerically using finite-element techniques. Experimental validation has been done on a cantilever beam with bonded polyvinylidene fluoride and lead zirconium titanate films. These equations are useful for developing techniques for shape control and active vibration damping in flexible structures.