Admittance matrix of asymmetric piezoelectric bimorph with two separate electrical ports under general distributed loads

The dynamic admittance matrix of the asymmetric triple-layer piezoelectric bimorph subjected to the general distributed harmonic loads as well as the flexural moments and the vertical loads at the tip are presented. The top and bottom piezoelectric layers have two separate electrical ports such that each layer can be used as either a sensor or an actuator. The variation principle is used for deriving the motion equations and the conjugate parameters that maintain the symmetry of the admittance matrix. The mechanical displacements and forces at the tip are expressed in a matrix form, which, together with the reciprocal condition, greatly simplify the analysis procedure. The derived admittance matrix under the cantilevered condition is presented by a five-by-five matrix, each row representing the relationships of the displacement and rotation at the tip, the volume averaged displacement, the separate electrical charges with the flexural moment and vertical load at the tip, the magnitude of the distributed load, and the voltages. The matrices, which reduce to simpler forms for several special cases, are then used to determine the two-port electrical admittance. It is shown that the derived admittance matrix covers the various boundary conditions, the electrical parallel and series connections, and the arbitrary lay-up, including the unimorph, used as both sensors and actuators.