Admittance matrix of a symmetrical triple-layer piezoelectric cantilever

A triple-layer piezoelectric cantilever, with one elastic non-piezoelectric layer sandwiched between two piezoelectric layers, can be used in piezoelectric actuators, sensing elements, and piezoelectric energy harvesters. This study focuses on a dynamic admittance matrix that relates harmonically varying exciting parameters: an external tip force F and an applied voltage V to their response parameters; these response parameters include the generated tip deflection δ and the electric charge Q. A 2 × 2 matrix links the tip force Fand an applied voltage Vto. The tip deflection δ and the quantity of charge Q. Thus, the tip deflection δ and the quantity of charge Q are obtained. The elements of this matrix are analyzed by MATLAB to describe dynamic characteristics between excitation and response of the triple-layer piezoelectric cantilever in the circular frequency ω domain. Calculations obtained through these elements in a matrix are consistent with the FEA estimations. Although ω is close to zero, results are consistent with existing models. The resulting model is applicable to predict structural dynamic characteristics, such as resonance frequency, anti-resonance frequency, displacement mobility, and dynamic capacitance.