Analysis of the asymmetric triple-layered piezoelectric bimorph using equivalent circuit models

An eight-port impedance matrix and an equivalent circuit are presented for the analysis of an asymmetric triple-layered piezoelectric bimorph with separate electrical ports. The separate electric ports for the top and bottom piezoelectric layers operate independently of each other: they generate and/or sense the coupled extensional and flexural motions. Taking into account shear and rotatory inertia, the eight-port impedance model is first obtained for the bimorph. The electromechanical behavior of the piezoelectric layers, and the mechanical motions of the bimorph, are separately represented by equivalent circuits with common ports. Connecting the circuits through the common ports then leads to the overall equivalent circuit. It is demonstrated that the resonance/antiresonance frequencies and the sensor-to-actuator signal of the cantilevered bimorph for various length-to-thickness ratios can be effectively calculated by the application of the electrical network theory to the equivalent circuit. It is also shown that the electric circuit conditions on the piezoelectric layers can alter the resonance frequencies of the bimorph without changing the mechanical conditions. All the results by the present method are in excellent agreement with those by three-dimensional finite-element methods.