Influence of Horn-Type Cavity Acoustic Coatings on the Error of Force–Sound Reciprocity Testing for Underwater Structures

Accurate measurement of vibro-acoustic transfer functions is essential for ship noise control. Because direct testing requires high-power excitation sources that are difficult and costly to deploy, the reciprocity method has attracted increasing attention. Its application to full-scale ships, however, has long been hindered by an unresolved theoretical question: whether hull-mounted acoustic coatings compromise force–sound reciprocity. To answer this question, this study combines theoretical analysis, numerical simulation, and anechoic water-tank experiments to investigate a typical horn-type cavity acoustic coating. Theoretical analysis shows that, because its complex stiffness tensor remains symmetric, a linear viscoelastic coating with geometrically asymmetric cavities still preserves reciprocity. Numerical simulations of a stiffened double-layer cylindrical shell covered with the coating show that the forward and reciprocal transfer functions coincide to well within 1 dB over the entire computed band. Anechoic water-tank experiments on a scaled model show that applying the coating raises the band-averaged reciprocity error by only 0.2 dB, from 1.4–1.5 dB to 1.6–1.7 dB in the 2–5 kHz band. These results provide evidence that, for the tested coating and structural configuration under anechoic conditions, the horn-cavity coating introduces no significant principle-based error into reciprocity testing—a first quantitative step towards removing the long-standing theoretical obstacle to applying reciprocity methods to coated, full-scale ships.