Sensitivity analysis for actuator placement on an Euler-Bernoulli beam

In this paper, we discuss the calculation of sensitivities for the cantilevered Euler-Bernoulli beam with piezoceramic patch actuators. The specific sensitivities in which we are interested are the sensitivities of the state to patch location and size. In particular, the continuous sensitivity equation method (CSEM) is applied to obtain the state sensitivities analytically via a partial differential equation. This equation is then approximated via a Galerkin finite-element scheme, and the approximations to the state and sensitivities can be computed simultaneously. Numerical results are given for a variety of patch locations and sizes.