# OS-E: 9000 Piezoelectric Analysis of a Cantilevered Bar

This example is used to demonstrate Piezoelectric Analysis using enforced voltage and enforced displacement using Linear Transient Analysis.

## Model Files

Before you begin, copy the file(s) used in this example to your working directory.

## Model Description

A cantilevered piezoelectric bar meshed with solid elements. In the first load case, the bar is subject to a sinusoidal electric potential at the free end. The applied potential triggers a structural deformation in the material. In the second load case, the output displacement from the previous load case is exported and added as input enforced displacement. This triggers the same voltage response, thereby demonstrating reverse piezoelectric effect.

## Boundary Conditions

The boundary conditions defined in the model are as follows:
• In load case 1, the sinusoidal voltage is scaled by an amplitude of 1000 kV and applied at the dependent grid of the MPC.
• In load case 2, enforced displacement (exported from load case 1) is applied on the same MPC grid, to study the output voltage.

## Material Properties

The material property definitions used in the model are as follows:
• Anisotropic Dielectric matrix (MAT2PT)
$\left[PMTV\right]=\left[\begin{array}{ccc}1.505& 0& 0\\ 0& 1.301& 0\\ 0& 0& 1.505\end{array}\right]{10}^{-8}farad/m$
• Piezoelectric coupling matrix (MATPZO) – Strain charge form
$\left[PIEZO\right]=\left[\begin{array}{cccccc}0& 0& 0& 741& 0& 0\\ -274& 593& -274& 0& 0& 0\\ 0& 0& 0& 0& 0& 741\end{array}\right]{10}^{-12}m/Volt$
• Orthotropic elasticity coefficients (MAT9OR)
E1
60.61 GPa
E2
48.31 GPa
E3
60.61 GPa
V12
0.512
V13
0.289
V23
0.512
G12=G23
23.0 GPa
G23
23.5 GPa

## Results

• Load case 1: Applied sinusoidal voltage
It can be noted that the applied voltage triggers a structural deformation which is also sinusoidal.
• Load case 2: Reverse piezoelectric effect (applied displacement)
It can be noted that the output electric potential (plotted at dependent grid of MPC) is identical to the applied voltage in load case 1, thereby demonstrating reverse piezoelectric effect.