脉冲波作用下竖直弹性板的水弹性响应

Hydroelastic response of a vertical elastic plate to pulse wave

基于线性势流理论,将流场分为3个部分:入射势与反射势部分、辐射势的记忆部分、辐射势的瞬时部分,竖直弹性板的时域振动基于模态叠加法,利用傅里叶与拉普拉斯变换求解流场控制方程,与板的振动方程耦合,推导得出波浪作用下竖直弹性板的时域耦合方程,并利用二级四阶隐式Runge-Kutta法求解方程。首先给定竖直板一个初始弯曲,得到的结果与解析解和数值解结果吻合良好,验证了方法的正确性。其次对脉冲波作用下弹性竖直板的响应进行研究,分析了板的刚度系数、质量系数、脉冲幅值和边界条件对其水弹性响应的影响。研究结果表明,刚度系数对板的振动频率影响很大,脉冲幅值与板的振动幅度正相关,两边固定时对竖直弹性板的疲劳损伤最严重。

Based on the linear potential flow theory, and reflection potential, memory section of radiation time-dependent elastic deflection of a vertical elastic the flow field is divided into three sections： incident potential potential and transient section of the radiation potential. The plate is described by the mode-expansion method, the velocity potential is solved by using Fourier transform and Laplace transform, and the implicit 4th-order Runge-Kutta scheme with uniform time step is applied to solve the coupled motions of an elastic plate and fluid. First, with an initial condition that the elastic plate is bent, the comparative results are in good agreement with corresponding linear analytical solution and numerical solution. Second, the hydroelastic vibration of a vertical elastic plate induced by the pulse wave is considered, and the effects of the elastic plate stiffness coefficient, mass coefficient, pulse amplitude and edge conditions on hydroelastic behavior are studied systematically. Finally, the following conclusions have been obtained： the stiffness coefficients have a great impact upon the vibration frequency; the vibration amplitude values have a positive correlation with the pulse amplitude values ; and the fatigue damage of the vertical elastic plate is the most severe when the plate is fixed on both sides.