Transmission of a flexural-gravitational wave through an obstacle in an elastic plate floating atop a two-layer fluid. Thin-upper-layer approximation

Low-frequency time-harmonic waves in an infinite elastic plate floating atop a two-layer fluid of finite depth are considered. Transmission of a surface flexural-gravitational wave through and reflection from a straight-line obstacle in the plate are studied analytically. Under a thin-upper-layer assumption, two-layer fluid is approximately replaced by a single-layer fluid with a special boundary condition at its upper surface. In a low-frequency range, the approximate results are in an excellent agreement with those obtained in the exact statement.