The lower picture is correct. Two sheets coming together do create a stiff structure.
A Static Structural analysis with a tip load in the -y direction will show some a tiny deformation downward as the top sheet stretches and the bottom sheet compresses.
An Eigenvalue Buckling analysis with a tip load in the -y direction will show the critical buckling load when the sheets go out of plane into a shape like mode 1 of the Modal analysis.
I didn't open your model to look at where the piezo material is and what direction that material is expanding in, but you can see that motion in a Static Structural analysis.
Modal analysis does not permit any nonlinear materials and has no loads.
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