VM237
VM237
RLC Circuit with Piezoelectric Transducer
Overview
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| Input Listing: | vm237.dat |
Test Case
A piezoelectric transducer consists of a simply supported circular plate of radius a and thickness t (figure a below) made of PZT-5A ceramic polarized along the Z axis. The circular surfaces of the plate are fully covered by electrode and connected in series with a resistor (R), inductor (L), and a source of constant voltage (V) (figure b below). Determine the voltage across the piezoelectric transducer over the time interval of 2 ms.
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Constitutive Matrices (polar axis aligned along the Y axis)
PZT-5A Dielectric Permittivity Matrix at Constant Stress [εT r]
PZT-5A Piezoelectric Strain Matrix [d], 10–10 C/N
PZT-5A Elastic Compliance Matrix [s], 10–12 m2/N
Analysis Assumptions and Modeling Notes
The piezoelectric circular plate is modeled with 10 axisymmetric PLANE223 elements (Figure 399: Finite Element Model of a Transducer). The constitutive matrices used by the 2D model are adjusted to orient the PZT-5A polarization direction along the Y axis. The electrodes are modeled by coupling the VOLT dof on the top and bottom surfaces of the plate. The resistor, inductance, and voltage source are modeled using the respective options of the CIRCU94 element. A transient analysis is performed to determine the time response of the circuit to the unit (1V) step voltage load. Numerical results are compared with an analytical solution, obtained using the Laplace transformation technique applied to an equivalent RLC-circuit, where C is the static capacitance of the piezoelectric transducer.
