Vibrational study of fluid-structure interaction is one of the most widely used cases in engineering. In various industries, the effect of fluid on the structure and vice versa is necessary to investigate such as shipbuilding, ocean energy sources, offshore structures, etc. In this paper, the dynamic behavior of a long rectangular plate located on a viscoelastic bed at the bottom of a narrow channel has been studied in detail. According to earlier studies, the muddy seabed of coasts attenuate the waves. Here we investigate the interaction between the gravity sea waves and the muddy seabed by modeling the seabed as a rectangular plate that located on a viscoelastic foundation which contains springs and dampers. The springs and dampers are attached at the bottom of plate to model the behavior of the muddy seabed. The governing equations of motion have been obtained and a new semi-analytical solution has been presented to solve them. The proposed model is validated against available literatures. Then, the influence of different parameters such as boundary conditions, plate's rigidity and mass, damping ratio, restoring force and different transverse modes on the vibrational behavior of the system has been investigated in detail. The effects of various parameters on the frequency response of the system have been studied in detail
