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The authors formulate a fluid-structure interaction model coupling a 2D Euler–Bernoulli beam with a weakly dissipative quasi-potential fluid to investigate how structural flexibility alters wave-driven inertial propulsion. Modal decomposition into rigid and elastic modes yields a fast reduced-order model by expressing fluid loading as modal impedance matrices. The analysis reveals that isolated single modes cannot produce net thrust, establishing that propulsion requires precise multi-mode interference that can be tuned to achieve both thrust amplification and reversal.
Elastic rafts cannot produce net wave-driven thrust through single-mode oscillation alone, proving that propulsion relies entirely on coordinated multi-mode interference that can induce both thrust enhancement and directional reversal.
Inertial propulsion in fluids generally arises from an unbalanced flux of momentum. For the case of wave-driven propulsion, momentum is transported away from an oscillating raft in the form of self-excited surface waves. While this mechanism has previously been analyzed for rigid rafts, the role of flexibility has yet to be investigated. In this work, we develop a fluid-structure interaction model for a periodically driven two-dimensional flexible raft resting at the free surface of a fluid. The raft is modeled as an Euler--Bernoulli beam and is coupled to a weakly dissipative quasi-potential model of the fluid beneath. Varying the flexural stiffness and forcing position reveals new features associated with the introduction of flexibility, including the possibilities of thrust enhancement and reversal. By projecting the raft response onto its free rigid-body and elastic modes, the fluid loading can be represented as a modal impedance, informing a computationally efficient reduced-order model. Analysis of the modal response and its symmetries facilitates physical interpretation of our key findings. For a uniform raft, excitation of any single mode in isolation is incapable of producing a net thrust, and thus efficient wave propulsion requires a blend of interfering modes with appropriately coordinated amplitudes and phases.