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Piezoelectric materials (PZT) are commonly used as actuators and
sensors for vibration suppression in flexible metal or composite
substrates. There are well-established techniques for modeling the
actuation of PZTs when they are bonded to these structures.
However, if the substrate material is much softer than the
piezoelectric actuator/sensor, a higher level of modeling is
needed to predict the local deformations at the interface.
In this research, a finite-length piezoelectric element bonded
perfectly to an infinite elastic strip is modeled. The specific
goal was to quantify the actuation and sensing mechanics of
piezoelectric devices on substrates potentially much softer than
the piezoelectric element. Previous works have addressed
membranes or plates bonded to an elastic half-space subjected to
mechanical or thermal loads.
Euler-Bernoulli beam theory is used to derive equations of
equilibrium for the piezoelectric beam. These equations are then
recast as integral equations for the interface displacement
gradients and equated to the equivalent quantities for an elastic
layer subject to distributed shear and normal tractions. The
resulting singular integral equations are solved by expanding the
interface tractions using a series of Chebyshev polynomials.
First, certain sanity checks are performed to confirm the validity
of the model by choosing a stiff substrate for which
Euler-Bernoulli beam-assumptions holds good.
For certain combinations of geometrical and material parameters,
the substrate has a positive curvature, whereas the piezoelectric
has a negative curvature and vice versa. After analyzing the
forces acting on both piezoelectric and the substrate, the reasons
for this behavior in soft substrates are justified here. Finally,
the range of geometric parameters where the reversal of bending
occurs in the piezoelectric is given.
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