Analysis of the dispersion spectrum of fluid-loaded anisotropic plates: leaky-wave branches

The supersonic complex-velocity versus real-frequency dispersion spectrum of the leaky waves in fluid-loaded anisotropic plates is discussed. Utilizing the sextic plate formalism provides approximate solutions for leaky-wave velocity in a form that reveals their basic features, such as the unique correspondence of the signs of its imaginary part and of the free-plate group velocity, the relation between the leakage and the rate of frequency dispersion, and the principal trends at low, high and near-cutoff frequencies in arbitrary anisotropic plates. A particular thrust of the study is the derivation of closed-form asymptotics for the fundamental leaky-wave velocity branch(es) at low frequency and for the continuum of leaky-wave branches near the fluid-coupled and fluid-uncoupled thickness resonances. Conditions for the asymptotics accuracy are analysed, and a comparison between an analytical approximation and exact numerical curves is presented for various cases.