Steady-state hydroelastic waves generated by a moving load in a uniform current

Abstract

Steady-state hydroelastic waves generated by a moving load with a uniform current are investigated analytically in the framework of nonlinear potential theory. Considering the load with an exponential distribution in horizontal direction, we focus on the wave dynamics characteristics when the relative current speed or the nonlinearity increases. With the aid of the homotopy analysis method (HAM), appropriate solution expressions for the unknown variables are established by comparing the relative current speed U and the minimal phase speed cmin of the hydroelastic waves. Our results demonstrate that, the wave deflection is symmetric about the load if U is much smaller than cmin. The wave deflection becomes more oscillatory and its amplitudes increase in the vicinity of the load when U increasingly approaches cmin. If U is greater than cmin, the hydroelastic waves will be generated far away from the load, and the period of the gravity waves in the downstream region are relatively larger than those of the hydroelastic waves in the upstream region. As U increases continuously, the amplitudes of gravity and hydroelastic waves all first increase and then decrease. It should be noted that there is a larger cmin of the approximate nonlinear dispersion relation than that of the linear one, and the variation of the nonlinear wave deflection would be underestimated if the linear dispersion relation is used. Finally, the graphical representations show the effects of several important physical parameters including the uniform current speed, the amplitude of incident wave, and the plate thickness on the hydroelastic waves.