Predicting wave force on vertically submerged rectangular thin plate in intermediate depth of water using second-order perturbation equation

Abstract

The present paper studies the nonlinearity effect of an ocean wave on a thin rectangular plate under two geometrical configurations in the intermediate water. The perturbation approximation method was derived analytically up to the second-order. Analytical results was validated by the numerical method of Simpson's 1/3 rule. Results showed that the horizontal force of the wave on a plate recorded at the water surface (<em>z/d</em> = 0) was significantly high for ε = 0.175 and <em>d/L</em> = 0.24 as compared to the low value of relative depth. The results also showed that the wave forces are gradually converging to each other under two types of geometrical configurations with the decrease of relative depth. Nonlinear effect of the wave forces on the plate in the form of double peaks was found in the graph at a low value of <em>d/L</em> = 0.10 and wave steepness ε (= 0.070). This study revealed that due to the effect of nonlinearity, greater wave force occurred at a depth <em>d</em> = 3 m and <em>T</em> = 3 s and <em>d/L</em> = 0.24 on a thin plate and also implied that this force does not occur at the stage of double peaks form.