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7.4  Example of MFC transducers integrated in plate structures

This example deals with a cantilever aluminum plate with two P1-type MFCs (M8528-P1) attached on each side of the plate. The geometry is represented in Figure 7.25. The plate is meshed with rectangular piezoelectric elements. The main part of the beam is made of one layer (aluminum), and the part where the two MFCs are attached is made of 11 layers (5 layers for each MFC and the central aluminum layer).

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Figure 7.25: Geometric details of the aluminum plate with 2 P1-type MFCs

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In d_piezo('TutoPzMFCPlate-s1') , we build the mesh, define the sensors and actuators, and compute the static response. Using the two MFCs as actuators, we define two combinations in order to induce bending or traction and compute and represent the static response in (Figure 7.26).

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a)                      b)

Figure 7.26: Static deformation under combined voltage actuation in a) bending, b) traction

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The deformed shape under traction actuation highlights the fact that the induced strain in the lateral direction is of opposite sign with respect to the longitudinal direction, which is due to the fact that we are using a P1-type MFC. F1-type MFCs are based on the same layout as P1-types but the fibers are oriented with an angle of 45 . Such transducers can be easily modeled by changing the angle of the active layer in the multi-layer sequence. Assume that the bottom MFC makes an angle of 45 with respect to the axis of the beam and that the top MFC makes an angle of -45 . Each actuator induces both bending and torsion in the plate.
This is done in d_piezo('TutoPzMFCPlate-s2') . The torsion can be easily seen by looking at the deformed shape resulting from the combination of the two MFCs with opposite signs which cancels the bending effect, as shown in Figure 7.27.

%% Step 2 - Rotate fibers
model.il(2,[20 44])=[45 -45];
d1=fe_simul('dfrf',stack_set(model,'info','Freq',0)); % static response
cf.def=d1; fecom('scd 10');  C2=fe_case('SensObserve - dim 2 3 1',sens,d1);

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Figure 7.27: Static deformation under combined voltage with opposite sign using two F1-type MFCs

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