Nonlinear responses of a horizontal plate under the water impact

Abstract

The water impact of an elastic plate is an important issue in numerous engineering applications. Despite extensive research on various aspects of this subject, the nonlinear behavior of the plate's response during water impact remains unexplored. In this article, the novel contribution is the nonlinear response analysis of a plate under compressive loading when impacted with water. The geometric nonlinearity caused by midplane stretching is taken into account. Hydrodynamic pressure is determined by the velocity potential function of the flow. A fully coupled nonlinear hydroelastic equation is derived as an integrodifferential equation. This equation is simplified to the Duffing equation by expressing the deflection as a linear combination of the dry mode shapes. The Duffing equation is solved analytically using Jacobi elliptic functions. Additionally, the fixed points of the Duffing equation are examined using phase portraits of the first mode shape to identify the effects of nonlinearity on the responses. The analytical solution is verified using the Runge–Kutta method and validated against the methods available in the literature. The effects of midplane stretching on the maximum deflections, bending stresses, and wet frequencies are evaluated for various horizontal speeds and compressive loads. The results indicate that the amplitude and oscillation period of the nonlinear response are significantly smaller than those of the linear response. Furthermore, it is found that midplane stretching should be considered in modeling the impact of the elastic plate on the water.