This paper studies the three-dimensional unsteady problem of the hydroelastic behavior of a floating infinite plate under the impact of waves generated by moving loads on ice plate in conditions of sloped bottom. An analytic solution of the problem is found by integral transformations and asymptotic expansions. The amplitude is analyzed for various values of bottom slope, basin depth, plate thickness, vehicle length, deceleration and acceleration coefficients.
The topic of moving loads on floating elastic plates is of interest in a number of practical applications: floating platforms, ice fields and so on. It is known that the flexural-gravity waves occurring during the load motion reach their maximum amplitude at critical velocities. Deceleration and acceleration of load introduce special difficulties. It is interesting to analyze an effect of sloped bottom and deceleration (acceleration) of load on plate deflection to prevent possible plate breakup. We note that the effect of the bottom topography has recently been investigated in the linear problem of the scattering of periodic surface waves by a floating elastic plate (Wang and Meylan, 2002; Sun et al, 2003; and Kyoung et al, 2005) on the assumption that the liquid flow and the plate deformation are periodic functions of time. Sturova (2008) investigated the behaviour of the plate for different actions and shapes of bottom irregularities. The ship motion over sloping bottom has been considered by Buchner (2006), Ferreira and Newman (2008). Kim et al (2010) considered the motion of floating barge and a LNG carrier in sloping bottom.
We now conduct an analysis of the applicability of the Eq. 11 to a calculations of three-dimensional flexural-gravity oscillations of floating ice plate using the experimental data obtained by Takizawa (1985) and theoretical data obtained by Bukatov and Zharkov (1997).