Dynamic Modeling Of Spherical Variable-Shape Wave Energy Converters

The paper models a spherical variable-shape WEC, defines the PTO as a pure heave damper with Qpto having only the heave component Q3 = −c ȧrsa,3 (its Eq. 91 and compact form Eq. 94), and then reports simulated heave velocity, generated power, and 60 s harvested energy. The reported ordering and ratios E(VSWEC0) ≈ 1.59 E(FSWEC), E(VSWEC) ≈ 1.57 E(FSWEC), E(VSWECπ/2) ≈ 1.228 E(FSWEC) are stated in the Results section (Fig. 8/Table 2) and textual summary, with radiation neglected and a uniform excitation pressure assumption . These support the qualitative claim that flexibility increases energy capture, but the argument is empirical for one parameter set and does not constitute a general proof. The model solution correctly identifies the PTO power identity p(t) = c ż^2 and integrates it to E(T) = ∫0^T c ż^2 dt, consistent with the paper’s PTO definition (implied by Eq. 91 and how “generated power” is plotted), and offers a plausible frequency-domain Schur-complement explanation for increased admittance and the observed ordering; it also reproduces the paper’s energy ratios with a simple SISO demonstration. However, it relies on linearization/passivity and hand-chosen Σ(ω) values rather than deriving them from the paper’s shell parameters, and it treats ratios as amplitude/time-invariant in a way that the paper itself notes may be affected by nonlinearity (phase shift). Hence, both the paper (empirical, specific scenario; radiation neglected) and the model solution (analytical but assumptive/illustrative) are incomplete.