Optimize thrust over stiffness and actuator position

Determine the local maxima, minima, and saddle points of the mean thrust of the two-dimensional flexible-raft wave-propulsion system over non-dimensional stiffness \(\kappa\) and actuator position \(x_M/L\), using the reduced-order modal model and the conditions \(\partial F_T/\partial x_M=0\) and \(\partial F_T/\partial \kappa=0\).

Background

The paper develops a reduced-order modal model for a vertically forced, flexible Euler–Bernoulli raft that generates asymmetric gravity–capillary waves. Numerical parameter sweeps show alternating positive- and negative-thrust regions in the plane of actuator position and flexural stiffness, with strong thrust enhancement near elastic-mode resonances.

Although the authors identify the equations needed to locate stationary points of the thrust landscape, they do not carry out the formal classification of local maxima, minima, and saddle points. The unresolved problem is therefore to use the reduced-order model to systematically optimize thrust with respect to both actuator placement and raft stiffness.