Determining Hydrodynamic Force on Accelerating Plate in Fluid with Free Surface

Abstract

An approximate solution for the hydrodynamic force exerted on a moving rigid vertical plate in an incompressible inviscid fluid is derived when the plate is undergoing long‐period motion. The first‐order solution for the velocity distribution is used to solve the equation of conservation of momentum locally on the plate and to derive the second‐order term of the pressure distribution. The hydrodynamic force is derived after integrating the pressure distribution. The lowest order and the second order of the finite‐amplitude solution is shown to agree with the linear theory and with the nonlinear/dispersive theory, respectively. In certain cases, this theory allows the calculation of the force from the plate motion directly. The theory is useful in calculations of wave generation, and it may be useful in calculations of the hydrodynamic forces exerted on dams during earthquakes.