Piezo-ElectroMechanical (PEM) Kirchhoff–Love plates

Recently, the concept of Piezo-ElectroMechanical (PEM) structural members has been developed by Alessandroni et al. (Int. J. Solids Structures 39 (20) (2002) 5279) and Andreaus et al. (J. Vib. Control (2004) in press). Given a structural member, a set of piezoelectric transducers is uniformly distributed on it and electrically interconnected by a circuit that is the electric analog of the host member. In this way a high-performances piezoelectric structural-modification is obtained, that aims to control multimodal mechanical vibrations (see, e.g., Vidoli and dellʹIsola (Acta Mech. 141 (2000) 37)). In the present paper the problem of synthesizing an electrically dissipative PEM Kirchhoff–Love (K–L) plate by using completely passive electric elements is addressed. This is done by using a discrete form of the Lagrange functional governing the motion of a K–L plate by a finite difference method. Hence a novel electric circuit governed by the obtained finite dimensional Lagragian is determined. Multimodal vibration damping is achieved by completing this new circuit with optimally dimensioned and positioned resistors. A realistic simply-supported PEM K–L plate has been designed and its performances in the case of free and forced vibrations have been studied to show its technical feasibility.