  Chains of resonators in the form of spring-mass systems have long been known
to exhibiting interesting properties such as band gaps. Such features can be
leveraged to manipulate the propagation of waves such as the filtering of
specific frequencies and, more generally, mitigate vibrations and impact.
Adding nonlinearities to the system can also provide further avenues to
manipulate the propagation of waves in the chain and enhance its performance.
This work proposes to optimally design such a chain of resonators to mitigate
vibrations in a robust manner by accounting for various sources of design
uncertainties (e.g., nonlinear stiffness) and aleatory uncertainties (e.g.,
loading). The stochastic optimization algorithm is tailored to account for
discontinuities in the chain response due to the presence of nonlinearities. In
addition, a field formulation is used to define the properties of the
resonators along the chain and reduce the dimensionality of the optimization
problem. It is shown that the combination of the stochastic optimization
algorithm and the field representation leads to robust designs that could not
be achieved with optimal properties constant over the chain.
