PDE-constrained optimization for vibration mitigation in active structures

In this work, the Lorentz force activated multi-field coupling mechanism is exploited for vibration mitigation in structures within the PDE-constrained optimization framework. Deterministic and stochastic PDE-constrained optimization problems for a composite plate subjected to mechanical and electromagnetic loads are formulated and solved, where the objective is to minimize plate vibrations due to a deterministic or stochastic mechanical load by applying an electric current with a specially constructed current density profile. The solution algorithms for the formulated PDE-constrained optimization problems are based on a black box optimization approach with an analytic adjoint-based method for computation of the gradient of the objective function. Given the computed gradient, a first-order method that alternates between a nonmonotone gradient projection algorithm and a regular unconstrained conjugate gradient method is utilized. The results of the conducted computational study suggest that effective vibration mitigation via an electromagnetic field is achievable with an optimally chosen profile of the electric current.