Rocking vibration of a rigid disc embedded in any depth of a coupled seawater-visco-poro-elastic seabed half-space

This paper models the rocking vibration of a rigid disc embedded in a visco-poro-elastic seabed, covered by a compressible inviscid seawater half-space. The behavior of water and soil are governed by Euler equations and the Biot׳s theory, respectively. The contact surface of the disc with the soil is smooth. The coupled rocking vibration problem is formulated using Helmholtz potentials combined with boundary conditions at the seawater-seabed interface and plane passing through the disc. With the help of integral transforms, the governing dual integral equations are changed to Fredholm integral equations of the second kind. The dynamic impedances for both permeable and impermeable discs are obtained with different embedded depths, soil conditions, and frequencies of excitation. It is found that when the embedded depth is larger than the diameter of the disc, increasing the embedment depth will not increase the rocking impedances any more.