Three-port impedance model of a piezoelectric bar element: Application to generation and damping of extensional waves

A straight bar element containing piezoelectric members is viewed as a linear system with one electrical and two mechanical ports where it can interact with external electrical and mechanical devices through voltage, current, forces and velocities. A generalized force vector, with one voltage and two forces as elements, is expressed as the product of an impedance matrix and a generalized velocity vector, with one current and two velocities, as elements. Due to symmetry and reciprocity, this matrix is defined by four of its nine elements. Two applications are considered for a piezoelectric bar element (PBE) that constitutes a part of a long elastic or viscoelastic bar, viz. generation and damping of extensional waves in the bar. In the first, the PBE is driven by a given input voltage or by the output voltage from a linear power amplifier. In the second, the PBE supplies an output voltage to an external load. In numerical simulations carried out for a specific laminated PBE, an elastic bar, a serial RL load and a bell-shaped incident wave, the highest fraction of wave energy dissipated was 8.1%. This is much less than the 50% achievable for a harmonic wave under condition of electrical impedance matching.