The hydroelastic interaction of water waves and the finite-length ice sheet with a gap is investigated in this study. The ice sheet is treated as an elastic thin plate with free-edge boundary conditions. The analytical solutions are obtained using the eigenfunction expansion method. Effects of the gap location on water-wave propagation and hydroelastic responses of the ice sheet are analyzed. Local minima and maxima are found in the transmission coefficient curve. Enhanced wave elevation in the gap and hydroealstic response of the ice sheet can be observed at specific wave frequencies. The wave resonance effect in the gap is also discussed.
With climate change, Arctic shipping routes have attracted great interest from researchers and the industry (Smith and Stephenson, 2013). The interaction of water waves and sea ice is becoming a hot subject at present. On wave-ice interaction problems, early researches have widely considered the situation of semi-infinite or finite sea ice in water waves, by assuming the sea ice to be perfect and continuous (e.g. Fox and Squire (1990), Fox and Squire (1994), , Meylan and Squire (1993), Meylan and Squire (1994), Sahoo et al. (2001), and Teng et al. (2001)). It is also common that an ice sheet may have cracks or a polynya in it, which brings more difficulties to the hydrodynamic analysis. Squire and Dixon (2001) found that the crack can behave as a steep low-pass filter that allows an easier passing through of long waves. The perfect transmission can also occur at some specific wave periods. Shi et al. (2019) found that both the length and distribution of the polynya have important effects on wave reflection and transmission. dependent on the relative position of the submerged body to elastic plate edges. Ren et al. (2016) studied the wave excited motion of a floating body between two semi-infinite ice sheets and observed standing waves in the polynya. Li et al. (2018) considered a circular cylinder submerged below an ice sheet with a crack. The results revealed that the location of the crack played an important role in the body motion.