We perform three-dimensional simulations of an elastic plate heaving in a sinusoidal motion with different frequencies to explore the effects of the forcing heaving frequency on the hydrodynamic force generation and flow structures. It is aimed to simulate the motion of a rectangular elastic plate, representing a simplified flexible wing or fin, placed in an open water tank as in a corresponding experimental study. The top edge of the plate oscillates sinusoidally in water at rest. Simulations are conducted for the fluid structure interaction of an elastic plate with a special version of the open-source library C++ OpenFOAM, foam-extend-3.2. The plate oscillates at different heaving frequencies in a range of 3.5 Hz and 4.5 Hz. Experiments are carried out to validate our simulations. The results are in a good agreement with the experiment in terms of the representation of the resonant frequency and the induced hydrodynamic forces. It is found that the hydrodynamic force and propulsive efficiency are mainly affected by the elastic deformation and forcing heaving frequencies. The generated thrust is observed to be significantly enhanced at the resonant frequency, while the propulsive efficiency is increased at the heaving frequency which is greater than the resonant frequency. The results of our simulations point to the importance of resonant flapping frequency for considering the optimal heaving frequency to achieve the best performance and to get the improved thrust force, which are crucial for the locomotion of birds, insects, fishes, flapping-based micro air and underwater vehicles.