The time-dependent solution of the two-dimensional linear water-wave problem is presented, in which a semi-infinite fluid region is bounded on one side by a vertical elastic plate. Utilizing the mode-expansion method for the elastic deformation of structure, an analytical solution of the problem is constructed by decomposing the hydroelastic problem into three parts. Numerical experiments show that the validity of the present method by comparing it with other time domain methods.
Hydroelasticity is the study of the interaction between fluids and elastic structures. One of the earliest work on this subject is a book written by Bishop and Price (1979). In the present paper, we concern the time-dependent hydroelastic problem of a vertical elastic plate, which is motivated by trying to understand both the motion of wave forced by the vertical elastic plate and how the vibration of the vertical elastic plate is affected by the presence of the fluid. It is worth to pay attention that the wave forcing of a vertical elastic plate can be used to model a wide range of marine structures; for example seawalls, LNG tanks, and breakwaters. For this reason, the hydroelastic response of a vertical elastic plate is investigated in this paper.
The time-dependent problem for elastic bodies has attracted a great deal of attention from many researchers. Approaches to the time-dependent hydroelastic problem can mainly be categorized into three species. The first is based on a memory effect kernel and is known as the Cummins (1962) method. The second is based on a time-dependent Green function. Because of the difficulty to calculate the time-dependent Green function and solve the integral equation, the Cummins method is more popular than the time-dependent Green function method. But the Cummins method can not express the transient process and require the frequency-domain solution. Recently, an alternative solution method to the time-dependent problem, which is known as the generalized eigenfuntion method, has been proposed by Hazard and Lenoir (1993), Meylan and Sturova (2009), and Meylan (2014). The generalized eigenfuntion is rather more general than the Cummins method because it can be used to both calculate the solution of floating bodies as well as fixed bodies. Furthermore, the Fourier (or Laplace) transform method also play a important role in the time-dependent problem of elastic bodies.