Finite-element modeling of a smart cantilever plate and comparison with experiments

The behavior of a cantilever plate instrumented with a piezoelectric sensor and actuator is described using finite-element modeling. To demonstrate the accuracy of the numerical model, a parallel experimental study was carried out in the laboratory for the same geometric dimensions. The two results are compared and show excellent agreement, demonstrating that finite-element modeling is a good approach for optimized smart structure design. A three-dimensional finite-element formulation is employed in the piezoelectric material region and a small neighboring region of the plate structure on which it is mounted. Shell elements, approximated by many flat-shell elements, are used in modeling the remaining part of the plate structure. Transition elements that connect the three-dimensional solid elements to the flat-shell element are used. For the cantilever plate example, the electrical input admittance as well as the sensor response are found from the finite-element analysis and they are compared with experimental measurements. From this, the accuracy and efficiency of this approach is demonstrated. In contrast to many other modeling techniques used for smart structures which are approximate and hence limited, the finite-element model is applicable to complicated geometries.