### ASA 125th Meeting Ottawa 1993 May

## 3pSA1. Asymmetric actuation and sensing of a beam using piezoelectric
materials.

**Francois Charette
**

**
Guy Plantier
**

**
Catherine Guigou
**

**
Alain Berry
**

**
**
*G.A.U.S., Mech. Eng. Dept., Univ. de Sherbrooke, Sherbrooke, PQ J1K 2R1,
Canada
*

*
*
The purpose of the present work is the modeling of a beam actuated by a
ceramic piezoelectric on the top with a PVDF piezoelectric on the opposite side
acting as a sensor. The two piezoelectric are different in types, may be of
arbitrary length and can be positioned independently along the beam. Since
there is only one actuator, the asymmetric excitation induces transverse and
axial displacement in the beam. This asymmetric actuation contrast with the
symmetric actuation normally considered in the literature. Symmetric actuation
implies no axial displacement. Here, both piezos are considered perfectly
bonded to the beam and the Bernoulli--Euler hypothesis is used for the
displacement field. The variational approach with Hamilton's principle is put
to use in the theoretical model. Hamilton's principle states that the definite
time integral of the Lagrangian shall be stationary. This formulation, which is
energy based, allows one to consider any boundary conditions and to take into
account the dynamic effects of both piezos on the beam response. The
theoretical model gives the axial and transverse displacements, the strains,
the mean quadratic velocity of the beam, and the voltage of the PVDF piezo
sensor as a function of the voltage given to the actuating ceramic piezo.
Experimental results are compared to the theoretical model for the case of the
beam with free-ends boundary conditions.