Normal wave diffraction on a plate submerged in a liquid: Level gauge model, factorization method modification, and waveguide quasiresonances

Abstract

An exact solution is obtained for onemore new diffraction problem whose transcendental difficulty has been known since Sommerfeld and Kirchhoff. The model of waveguide level gauge, where the main problem is the bulk diffraction of normal waves in a layered structure consisting of an elastic plate between two semi-infinite liquid layers, is investigated. The boundary value problem is solved by using a modification of the Wiener–Hopf factorization method; the factorization is used twice to solve two systems of underdetermined functional equations, and this is a specific characteristics of the problem and amethodological novelty. The proposed modification is acceptable for the class of such problems. The diffracted spectra are analyzed; the waveguide quasiresonances are physically treated; the effect of pure Lamb wave propagation under the liquid is established; the narrow-band backward-wave modes are determined.